Yes to running water! I think you're right and he just needs to get over that one hump of peeing in the potty rather than his clothing/diaper. It does sound like he's ready!
Run the water in the sink or bathtub (whatever is closer to him) while he's sitting on the pot. Or get a bowl of warm water and let him put his hands/feet into it while sitting on the pot. Or if you have a shower head that reaches, run warm water on him while he's sitting on the pot.
Wish someone had done that for me when I got my catheter out after my c-section.
Or get him a book or other distraction to play with on the pot.