Try practicing swings with those regular straps, to get used to it. But if you can't get used to it, you can get the Deitch grips Ultimate Strap - they go around your wrist with their own leather wrist guard, and attach with velcro. You can get them online, they are listed on the Gym Chat listings & ratings directory:
http://www.gymchat.com/listings/details.php?listing=267 (it's under the gymnastics grips category, that is the direct link)