If you don't wear gloves, start. If your bars are wrapped, wrap them. Now rais the stem so that you can sit comfortably in the saddle without your hands supporting any of your weight, simply providing balance. This will probably be right around equal height or maybe even with the stem a centimeter or two higher. It may be useful to get some swept back cruiser bars.
I've ridden with stitches in my hand, but not on the palm. Good luck.