Here's a link that might help. I know it's using birds as an example, but it might be a place to start --
Bird-safe Paints
I would say that child-safe paints would probably do the trick (I'm no expert so don't take that as definite). Like, what you'd use to paint a baby's crib or whatnot.
Sometimes paints can take more than a few days to dry throughly and not emit any more fumes. Just because humans can't smell them doesn't mean the pigs won't be able to. Considering cavy lungs are a lot smaller than human ones, I'd say it wouldn't take much to damage them. I'd leave it for a week before I replaced it, to err on the side of safety.