Q:

Which "Walker" is Thoreau referring to in "A Plea for Captain John Brown"?

“If Walker may be considered the representative of the South, I wish I could say that Brown was the representative of the North. He was a superior man.”
Excerpt From: Henry David Thoreau. A Plea for Captain John Brown.

Who was Walker?

A:

Question:
  “If Walker may be considered the representative of the South, I wish I could say that Brown was the representative of the North. He was a superior man.”
Excerpt From: Henry David Thoreau. “A Plea for Captain John Brown.”
Who was Walker?

Here the entire paragraph which contains that sentence, which is the only reference to Walker in the essay by Henry David Thoreau.

A Plea for Captain John Brown
If Walker may be considered the representative of the South, I wish I could say Brown was a the representative of the North.  He was a superior man.  He did not value his bodily life in comparison with ideal things.  He did not recognize unjust human laws but resisted them as he was bid.  For once we lifted out of the trivialness and dust of politics into the region of truth and manhood.  No man in in American has ever stood up so persistently and effectively for the dignity of human nature, knowing himself for a man, and the equal of any and all governments.  In that sense he was the most American of us All.  He needed no babbling lawyer, making false issues, to defend him.  He was more than a match for all the judges that American voters, or office-holders of whatever grade, can create.  H could not have been tried by a jury of his peers, because his peers did not exist."

Answer:
Walker is David Walker a famous, influential abolitionist from North Carolina who left the south and moved to Boston five years before his death.  Walker was among the most radical of the abolitionists who along with John Brown shared the idea of destroying slavery by inciting black revolution which placed them at the extreme of the abolitionist movement. 
Walker in leaving the south spoke of his discomfort being in the presence of slave holders and expressing concern for his own life if he had stayed in the south.  

David Walker
  "If I remain in this bloody land, I will not live long...I cannot remain where I must hear slaves' chains continually and where I must encounter the insults of their hypocritical enslavers."

.
The paragraph in question uses this to draw a comparison between the two fire brands of the abolitionist movement ultimately elevating John Brown.
John Brown who had helped David Walker publish his 4 part essay which made Walker famous among abolitionists and infamous in the South, Appeal to the Colored Citizens of the World.  David Walker who like John Brown called for slaves to violently resist slave holders, is credited with radicalizing the abolitionist movement through his writings and essays.  Something else which Links Walker and Brown was the fact that 2 years after David Walker published his essays 1830, promoting slave rebellion Nat Turner revolted 1832 in the south killing 49 white southerners.  Nat Turner, John Brown and David Walker are thus linked in history and among abolitionists like Henry David Thoreau as being among their most extreme practitioners prior to the civil war.
In the sentence given, Henry David Thoreau is about to proclaim John Brown most exceptional because he stayed endured the discomfort which Walker had retreated from and ultimately gave his life for his ideals. Thoreau does this not to diminish Walker, but to promote Brown; the subject of his essay.  John Brown at the time was getting lambasted in the press as insane and worthy of being mocked;  Here Henry David Thoreau is saying, no no;  John Brown was the best of us, exceptional, and here is the reason why.   In order to do this he contrasts John Brown with one of the Abolitionists most respected and influential practitioners;  David Walker.

Background
Captain Brown refers to the militant abolitionist John Brown who lead a raid on the Federal armory at Harpers Ferry in what then was Virginia, in a failed attempt to start a slave rebellion.  Brown was executed on December 2, 1859.  Brown's raid was one of the harbingers of the American Civil War.  Henry David Thoreau's in his essay, "A Plea for Captain John Brown" defends John Brown as an exceptional man to be placed above other exceptional men like Walker.

Answers to Comments: 

@T.E.D. Arguments aside, this answer asserts a specific person. Is there any documentary evidence (from say historians or contemporaries) that this is the person Thoreau was referring to? Or is this just personal logic and speculation?   

5 part response:              

I have found a source which I previously presented which identifies Walker from Thoreau's essay as David Walker and could find no source identifying Walker as William Walker.  Nor have you presented any.

Encyclopedia Brown, John And Henry David Thoreau
  Walker: David Walker (1785–1830), a black abolitionist who urged slaves to use violence to win freedom.

This article on Thoreau and Violence from the Thoreau Society says “A Plea for Captain John Brown.” was a response to the Luke warm praise John Brown received from William Loyd Garrison in the premier abolitionist newspaper of the time, The Liberator.  Garrison called Brown's raid "misguided" as well as "wild and futile".  Brown it says drew his inspiration from David Walker, and Thoreau it says in writing his essay was answering Garison's faint praise in an response to the abolitionist community. 
Brown and David Walker are linked in history.  Beyond expressing the same radical even for an abolitionist ideal of arming slaves to promote the violent destruction of slavery by murdering white people.  John Brown helped finance David Walker's 4 part Essay, "Appeal to the Colored Citizens of the World".
The pro slavery action hero William Walker doesn't make any sense in the context of the sentence or the accompanied paragraph.   John Brown was "superior" for placing his ideals above his physical comfort and safety while actively living by his professed morals.  The distinction is lost when contrasting William Walker and John Brown given William Walker was orders of magnitude more successful in conquest than John Brown who only succeeded in holding the Harper's Ferry armory for a number of hours.  William Walker created and was President of 3 republics his final one Nicaragua he ruled over for nearly a year.  The comparison in the paragraph, however; draws a direct contrast to David Walker and John Brown.  David Walker who shared Browns ideals but left the south in favor of the relative comfort and security of the north.
This essay Angel of Light: Interpreting John Brown,  also ties John Brown and David Walker together. As well as other anti slavery revolutionaries.

Gabriel Prosser (Virginia, 1800, 
Denmark Vesey (South Carolina, 1822)
Nat Turner Virginia, 1931
Henry Highland Garnet (1832

A:

I don't know, but one possible candidate would be William Walker (1824-1860) who led several private military "filibustering" expeditions into Central America to establish new slave states for the USA.  He made himself president of Nicaragua from 1856-1857.
He was born in Nashville Tennessee, and usually lived in the South, so he could be considered a southerner.
https://en.wikipedia.org/wiki/William_Walker_(filibuster)1

