Q:

Is a player required to ship on a wharf if they are able to?

In Puerto Rico, a player is required to ship as many of one good as they can in turn order.  
If a player has a wharf, goods available to ship, and is otherwise unable to ship goods on the available ships, is that player required to use their wharf to ship all of one of their remaining goods?  Or are they allowed to, say, hang on to their coffee to sell during a later trader phase? 

A:

No,
Using the Wharf is optional, and a player is not required to use it each turn.  Here are a couple quotes from the rules.
The Violet Buildings (page 9)

A player is not required to use the special function of an occupied violet
building if he does not want to (important with the wharf, see below).

The Wharf (page 11 - emphasis, mine)

The wharf can only be used once per captain phase by its owner, but he
may choose when to use it, if at all.

