Version 4.10 has now been released. I cannot guarantee that it will solve your problem, as I don't have a WAP test environment, but the only reason I can think of that it would not would be if the browser being used in the WAP environment does not accept Cookies.
I have added a Sticky option to the "For A Query Keyword=Value on any Page, Post or other non-Admin page" Settings section that sets a cookie for a year in the visitor's browser whenever the specified Query Keyword=Value occurs in a WordPress URL being viewed. And will always use that Theme for that visitor using that browser on that WordPress site. Until another Sticky Query Keyword=Value occurs. Or the Setting is changed. Or the year expires.
I am setting this Support Thread to Resolved, but that does not in any way stop you from responding, or me seeing your response if you require additional help or run into any issues.