Q:

"you would not be prepared to swear to me" Swear what?

I’d like ask about the sentence from The Naval Treaty by Conan Doyle.

“How are you, Watson?” said he, cordially. “I should never have known
  you under that moustache, and I daresay you would not be prepared to
  swear to me.

The speaker Phelps met Dr. Watson for the first time in many years in this moment. 
I can understand the first half of his remark, but what does “I daresay you would not be prepared to swear to me” part say? 
The first part is “Hello, I’ve never seen you with that moustache before.” or just “Oh, you’ve come to wear such moustache? I didn’t know that.” when you paraphrase this, right?
So the last part has to mean like “And I think I should look unfamiliar to you since it’s been many years since we last met.” But does it say so, with this “I daresay ..” stuff? I don’t know. 
Can anyone paraphrase the last part for me or tell me what the object for the verb “swear” , if the verb is being used as a transitive verb here?  Thanks. 

A:

This is an unusual use — or now an unusual use — of swear to:

swear to phrasal verb

To affirm with an oath; to express assurance of the truth of (a statement), or the identity of (a person or thing), by swearing.

1908   R. Bᴀɢᴏᴛ Anthony Cuthbert xxiv. 315   You could swear to its authenticity, or the reverse, if necessary?

— OED

That is, just as swear to its authenticity means "to make an oath that it is authentic"; this use of swear to me means "make an oath that I am me."
It doesn't indicate that the speaker is administering an oath (as one might swear to a magistrate to do something).

