Which: rivet or re-weld?

I have an old Jon boat, from Sears, that has a bunch of leaky rivets. In the past I had one of these boats, not a Sears but almost identical that also had leaky rivets. I re-set all of the leaky rivets and after a few years some started to leak again. No surprise there. So with the boat I have now I'm thinking of MIG welding around all the rivets on the outside of the boat and then running some beads on the inside bracing because some of the rivets will be loose. I know the welds will add some drag but I really don't care, the only bodies of water this boat will be going in are small so even if the motor quits the rowing distance will be short. Opinions? Thanks, Eric