[MunchkinMan]

Hmmmm. I'm going to say that the Cheat! is on Poop Deck, not on the Ship, so it only affects Poop Deck.

However, the Ship Enhancer is attached thus: If the Ship goes, the Enhancer goes. However, one can normally detach a Ship Enhancer in order to discard it (not trade, not move to another Ship, but a discard) in order to sell it, or for Curses/Bad Stuff which say you must discard Items or cards.