If it offends you, don't sing it. If you're singing it as a "Yeah, life was good in them days!" then you shouldn't be singing it. If you're singing it because of the lyrics/tune then it's like any depiction in a medium, which is to say it should be used with care and you should be able to explain why you're singing it.

Also, "Lady gay" I thought was a way of getting an extra syllable out of a line when you needed one, and thus didn't mean gay. It's like "He went down the street all fine and gay" isn't it?