| Buy that boy a leash! ...And train him to it.
It sounds harsh but a toddler leash is a viable means for parents who find they need them. I would highly recommend one for your son considering you have lost ability in your hands. This would greatly increase your son's safety and reduce your stress levels.
In this case, an ounce of prevention is worth more than a pound of cure.
To train a child to hold your hand or to a leash, begin by holding their hand or placement of the leash. This act will signal what is expected to the child.
Start by walking around the room, in the yard, or on a sidewalk. This is practicing.
When they resist [and most will!] you have to demonstrate who the boss is. When I use this technique with my 2 year old, because he would often run away or try to sit down every time. I would hold his hand firmly gently pulling up, and also his elbow with my other hand, creating a pulling effect on his arm while leading him around.
His mind is dealing with what is going on with his hand, while his feet and body go on auto pilot. In a sense, you trick them into the behaviour, and by repeating this [and offering a reward, if needed], you will program your child's behaviour. Thus, when in public, he will operate like he has practiced. It is the same thinking behind practicing an instrument, "you play like you practice".
In the leash scenario, walk him around allowing him to lead at first. Then begin to direct his travel. Should he resist, just stand there and allow him to throw a fit until he's done and begin again. The idea is he will tire himself out and eventually submit willingly. When he does, reward him accordingly.
Requires a lot of patience, but worth the effort in the end.
One of my philosophies with people in general: Reward the behaviour you want to see repeated and gently correct and pay little attention to behavours you dislike.
Best Wishes! | 
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