Actually I think a weapon like this should be given to the heavy. Take away his minigun, but give him a buttload of extra health so that he can go on a punching rampage.
Actually, that i exactly what I would like to see on heavy, give him a wearable weapon that replaces his minigun, that increases his health by 100% (giving him a grand base health total of 600 hp) and gives you a movement speed increase when you take (ranged?) damage. Oh, and you take 500% more damage while using anything other than your melee... aka your secondary. That would make it so that you can't try to be an op shotgun heavy, and would make you even more vulnerable while trying to eat your sandvich.