Sorry if I wasn't clear. I was committing to make my plugin look for the cookie on every WordPress "webpage" displayed, and change the theme if the cookie is there.
Since I wrote that, only issue that has come to mind is the possibility that a visitor (in your case, one of your WAP visitors) may have their browser set up to refuse cookies. I don't even know if that is possible, as I have no knowledge of WAP.
Only other point is a small thing that I would add if you need it or not. Calling the Function with no parameters would delete the cookie and have my plugin go back to normal behaviour.
I guess I should also mention that the Cookie (if present) would override any theme choice that the plugin would otherwise make.
Only design point I'm not sure about is "how soon" the function call would take effect. In other words, should my plugin Refresh the current page with the specified Theme?