Switch themes by cookie

I have a wp install that works with my main website. I’m testing out a redesign by giving a cookie (let’s call it x=1) to some users and that cookie is seen by the php on the main site and makes them see the new design instead of the old one.

I made a wp theme that matches this new design and I want to assign it to users who come into the blog with that cookie so that if they have x=1, they’ll see a “theme2” version of the blog rather than “theme1”. What is the simplest way to do this?

If you don’t know how to do it but know where to start looking. Any help would be appreciated.