There is no issue. Recently Cryptic changed the system so that all you need to do is select a small craft as your designated active small craft. If you go to the episode starting area, you will switch to your shuttle automatically, without having to switch ships at a shipyard. This is the same for Operation Gamma and Vault Ensnared.
TBH, being forced into a ship (or config, role, item, spec etc) that I haven't chosen to play is a bit of a pet peeve of mine.
See a shuttle in my ship inventory? No, you don't.
Then what makes you think for 1 second I want to fly one? Oh, you think I'd enjoy it if I "just gave it a chance".
What makes you think I'd somehow magically enjoy being FORCED into one then? Oh, you're intellectually challenged... got it.
This should have been a Lieutenant quest IMO, not Commander-ish. At least then I'd be forced out of the starter ship and into a soda-can with engines taped to it, instead of the ship I spent the next 2 dozen levels building. Might have actually enjoyed it that way.