No, the interface for picking cards is really bad with shelters and ruins.
If the card is in the supply (or is one of the available non-supply piles, madman/mercenary/spoils), you can just click on the pile. But if you want to name another card, you click on "name another card" which gives you a list of ALL OTHER DOMINION CARDS, sorted alphabetically. So if you want to wish for Hovel, you'll find it in the long list of cards, between Horse Traders and Hunting Party.
It's adequate, since it's not THAT frequent of an occurance to need to wish for a non-supply card (and since it'll work fine, rules-wise, when Black Market is available!) but it's still annoying. People would complain at Goko for that.
As it is, it fell completely off my radar because it's been so long since I had a game with both a wishing card (Wishing Well, Mystic, are those it?) and either shelters or ruins and careful-enough deck tracking that I'd want to wish for a one of those.
It's a more minor issue though, IMO, because usually you don't want to wish for a rare card like that, and so I think lots of other fixes should take priority. Rules-wise, it's perfectly fine as it is, and gameplay-wise, it's a rare situation.