Page with alternate template/theme

I need a page on my site that has it’s own background and no header. I have tried several squeeze and landing page plug-ins but they are very specific and not too flexible. All I need is to have my Contact Form 7 sign-up form on a page with its own background and no header or sidebar.

I’ve also tried the ‘blank template’ option but that is not much of a solution either.

Any ideas?