I think this is a recipe for disaster no matter what tang you get or how big it is. You have a resident yellow tang in at most a 4 foot long tank. By now it think it owns that tank. There's no amount of rock work rearranging you could do in such small of a space for it to think it wasn't its tank.
Purple tangs are the same genus, with a nearly identical body shape. I would be shocked if within moments of adding the purple to your tank one of them wasn't seriously injured. At the very least you're going to be dealing with constant, mid-level aggression between the two, with the dominant one keeping the subordinate one in a near constant state of stress.
I've tried to do what you're doing in 90 gallon tank. It didn't matter what species, or what genus, Zebrasomas were utterly intolerant of another tang in a tank that size. There might be people on here who've gotten away with it for a time, but the chances are good this is not going to work long term.
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