Sword Ping! Perhaps a little tardy but better late than never. Interesting observations about the injuries to Richard III.
So the story goes that Richard’s horse became bogged down in mud, so he dismounted. He was fully armored but at some point had lost (or removed) his helmet.
Those “shaving” or glancing wounds to the head almost have to be combat injuries sustained while fighting some one (or two, or...) probably armed with a longsword. Somebody almost got him with a zwerchhau, sounds like. Maybe even a couple more hits in addition. Seems that at some point he knew he was beaten. Perhaps disarmed. Knelt down and took the final blow with his head bowed. That weapon they say may have been a sword but I would submit that then it would have been more likely to decapitate him. Which it didn’t. A more likely implement would be something like a war hammer, or some such tool with a spike or point on the back. Short handle for use up close. Like a halberd head, but a halberd would be too long and unwieldy to do a precision execution.