Hi T.,
Ok. A couple things.
If it's an issue of him not quite being stable yet, but enjoying the attempt, I'd guess he doesn't want to hold your hand because it throws his balance off. If that's the case, try loosely tying an old scarf (pashmina) or a folded up twin bedsheet around his chest under his arms with the tails behind him. You can hold on to the tails, pulling up a little to give him support - but he can still fully use his arms for balance. My son loved that!
If it's a matter of him wandering away from you - I have to admit - we bought a "leash". It took me facing a flight with a layover travelling alone with my son (then about 2) to break down & do it. But, I knew he'd need to run off some energy and I didn't want to lose my mind - or him - in the airport.
Our son still enjoyed stroller rides when we were in public places - so that was our work-around to the independent streak. He could walk, holding our hands, or he could ride in the stroller. And, if he was stubborn about chosing neither - we went home. He figured out really quickly that wasn't fun. And, Love & Logic is great. I am a huge supporter of only giving your kids the pick of choices that you approve of!
Also - you might try holding Daddy's hand to show him it's something to be enjoyed, not some kind of control or punishment. I'd tell my son, as I grabbed his hand "I like holding your hand!" and now he tells me the same thing sometimes. It's the funniest, cutest thing! :) Especially remembering some of the battles we had over hand-holding!
So - I hope you find what works for you. Stick with it!