The choice of the word "ship" is the odd thing there. The intent of the display case is obvious enough, familiar from the general military setting of the 20th and 21st century Earth. But I'd think most of the space service officers who would have desktop or shelf models would have "rockets", "spacecraft", perhaps "planes" there. When did the idea develop that astronauts would be operating "ships"? There's no indication that Lily or Cochrane would have considered their warp test rig a "ship".
Then again, Picard does mention his "ship" repeatedly in conversations with Lily. In the "sounds Swedish" discussion, Lily is already familiar with the nomenclature and asks how big Picard's ship is. It should then be a fairly obvious leap to thinking that Picard's little models are ships, regardless of what they look like. Although I'd still think there would be a 50% chance of Lily thinking that those things might be spacecraft being carried aboard Picard's ship, the way an aircraft carrier skipper might display F-18 and A-6 models there.
Timo Saloniemi