All-wood bows generally have a really low brace height, around 5" or so, so the limbs don't get strained too much. When you release an arrow, the string will always come a short distance beyond brace height before the limbs stabilize. That's true of all bows, no matter what type. That's why string dampers like the STS are so popular on compounds. Not much you can do about that on a selfbow except to raise the brace height a bit. Don't raise it too much though. Having the brace too high will shorten the bow's lifespan.

Besides having properly spined arrows, another thing that can ease up the wrist sting is to make sure your arrow nocks aren't too tight. If they grab the string too tight, the arrow will pull the string even further past brace height before the nocks release. You want the nocks just tight enough that they will hang from the string, but loose enough that they'll fall off if you thump the string with your finger.

Also, going up in arrow weight will help.

I can't recommend it if the bowyer doesn't, but I've used fastflight strings on selfbows with no problems, and it really helped with that bit of wrist sting. If you choose to go that route, remember that I said you do so at your own risk.

If all else fails, just wear your armguard lower on your wrist.