Separate theme for one page

I’ve got the vast majority of a WordPress site built; the layout’s done, the blog and main content pages are done too, and displayed in an iframe on the main page. I also want a second iframe in another section that displays a particular page. Same page every time, but I need the ability to edit it in WP. It needs to be displayed with a different theme to the other pages though, since it’s got considerably less space to play with.

Anyone know how I can change the theme for this one page? Even if it means writing its own PHP page, that’d work just fine for me, but I don’t know exactly how to specify which theme it should be using in that code.

I tried renaming my index.php to another filename and defining define(‘WP_USE_THEMES’, true); as false, thinking I could insert a CSS stylesheet in to deal with the themes, but then it just stopped displaying any code whatsoever in the browser.

Cheers all.