Since the same replacement switches fit both, I am assuming the Stinger cover is like the one on my Ultrastinger. It can only be replaced by removing the entire switch assembly. The button cover is a fairly small part of the larger rubber cover that is part of the switch assembly. I'm not even sure if the cover is available seperately. When I needed to replace a bad switch in my Ultrastinger, the replacement assembly included the rubber cover.
Here's a copy/paste of an old post of mine, that started out asking the same question, but got no answers as far as how to actually remove the switch and replace the rubber boot. So I gave it a try, anyway. Only takes a minute once you know what to do.
"Got it out.
When you look at the light with the reflector removed, and switch pointing up, there are two "ears", for lack of a better word, that stick out toward you on the left and right. They both have a slot in them that you can pry on with a screwdriver. They have to be pried in a little, because they are overlapped by the threads inside the head. By putting the battery in, and pushing on it while prying in first one ear, then the other, the whole assembly started moving out. It got stuck part of the way out, but I stuck a screwdriver in the switch hole, and pried it the rest of the way out. I don't know what kind of plastic the switch assembly is made of. It's hard, and not very flexible, so I was afraid of cracking it, but it came through ok, and popped right back in when I was done.
Getting up the guts to pry on it was alot harder than actually doing it."