Wolverine, Best There Is + Menace and assigning damage question

If My Wolverine on the field has Menace, and my oponnent blocks with two creatures, lets (lets say two 0/2 creatures), can I assign 1 damage to both creatures, and since Wolverine effects doubles any damage he would deal, both creatures die? Or do I HAVE to assign 2 damage at minimum to one creature, so then then only the one creature dies, having been dealt 4 damage? I know that while assigning damage I have to assign at minimum lethal damage, and I don't know if that takes Wolverines ability in account.

Im pretty new to magic so sorry if I got something wrong, please feel free to correct me.

Thanks!!