I meant pure unarmed/melee no guns, explosives, energy weapons of any kind. I'm roleplaying that this guy really hates weapons of any kind and likes to get up-close and personal with his enemies, even if it's a Deathclaw.
In that case, I'm not sure how good you are with timing/depth perception, but could feasibly joust a Deathclaw to death, provided you block well enough when your lunges fail to stun.
My Juggernaut build is pretty much doing this, except she's rocking a ballistic fist and constantly hopped up on Psycho, so I usually get their attention, get the primary lunge, and beat it to death before the stun wears off.