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