You can do a strapless wrap carry on your front as well as your back. The key is having a way to load your baby securely while you wrap … when you do this as back carry, you can bend forward to make your back like a table … obviously, though, bending over backward while you wrap is not the way to a front torso carry. The trick is to start off as if you’re doing the front wrap cross carry, then one by one convert the shoulder straps to torso straps.
Here’s a video showing how to do this carry with a Moby Wrap. The same technique works with woven wraps, too. Enjoy going strapless!