chromed plastic isn't all that scratch-resistant. in a week you'd have something really super crappy. even on steel, chrome plating comes off quite easily.
plus, i can see it being really weird to hold, almost "sticky". although, the rough finish on the back of the psp makes it really slippery, so maybe that's a good thing.
maybe you could get one of the silver-colored shells and buff it to a shine. quite a bit of work getting all those little corners though
edit: the skins that lurkio linked to are a good idea, and probably the closest you're going to reasonably get. welcome to fingerprint city though.