No matter how ya slice it or whatcha call it...cheating is cheating and it sucks. I used to do it until someone did it to me and I found out how much it hurts to be on the other side. If you want your new relationship to be a healthy one, I'd suggest handling the one you're in first. Even if it means ending it.
I don't mean to sound like some bible thumping morals freak...I'm not. I'm sure there are exceptions, but I owned a detective agency for years and never saw a relationship that started from cheating end in anything but disaster.
Maybe you should give your current a shot...who knows, he might like a chance to take a riding crop to you!