You target three permanents as you cast Wild Swing. You don't randomly choose which one will be destroyed until Wild Swing resolves. If one of those permanents has become an illegal target by then, you randomly choose between the other two. If two of those permanents have become illegal targets by then, there is no random choice -- the remaining permanent is destroyed.

As Wild Swing resolves, there is no time to react between the time a permanent is chosen at random and the time it's destroyed. If you want to put a regeneration shield on one of those permanents, or sacrifice it for some effect, or anything else, you must do so before Wild Swing resolves (and before you know which one of the permanents will be chosen at random).

If one of the targets has indestructible, it can be chosen at random but nothing will happen to it if it is.