I want to be able to click a button on the home page that links to and starts a .exe slideshow file.

That's dangerous. Unless I'm missing something. First, I think, the .exe would have to download before playing. Most virus and trojan programs attach themselves to these type files. I personally would never click a link, or allow one to run an executable. Might just be me. Why not use a simple jquery slideshow for your pics ?

I agree. No browser will allow it and you could get your website flagged as malicious. I strongly agree you find other alternatives.

http://visuallightbox.com