Interesting question! Yes, you can do this with a small code modification. I see you're using version 1.2 beta, so look at qa-page.php (older versions should see qa-index.php). Where you have this line:
$themeclass=qa_load_theme_class(qa_get_option($qa_db, 'site_theme'), $qa_template, $qa_content, $qa_request);
Replace it with this:
$qa_theme=qa_get('qa_theme'); // get from URL parameter if possible
if (!isset($qa_theme)) // otherwise get option
$themeclass=qa_load_theme_class($qa_theme, $qa_template, $qa_content, $qa_request);
The other issue is that you will probably want the theme to be passed from one page to another, if the user navigates around. So to do this, you would modify qa_path(...) in qa-base.php, and add this at the start:
This won't work for Ajax voting, but that won't matter if both themes use the same layout for the voting boxes. There might also be some other places where it doesn't work right, so please try it out and report back!