One option to try is to use PlayOnLinux (Wine), install your .exe under it and use it's IE browser; just make an icon on Linux desktop to launch IE...
For more info, check out:
PlayOnLinux will allow you to play your favorite games on Linux easily
www.playonlinux.com
I'm using it with ThinkOrSwim to watch CNBC live while checking out stocks, the Linux version of ThinkOrSwim doesn't have CNBC live, as it requires mediaplayer. Tried installing H&R Block tax software, but it's a no-go under PlayOnLinux/Wine.