In that case, I think this is Caleb's match to win.
He's quite regularly fought gargoyles who fly using wings, and although the game's engine wasn't advanced enough at the time to really show off what their actual flight patterns would have been like, it's safe to assume that their mobility would be true to that of any other winged being. The advantage of flight won't matter much anyway once the Voodoo Dolls come out.
Other than that, I feel like Caleb's options are just more reliable to use in a fight. The hypnotising watch (Which I actually found a video of just now. Funny stuff) is a lot less usable in combat than Caleb's weapons and magic artifacts, and while only half of Caleb's weapons are 9-A, a great deal of Conker's more useful weapons are things our Chosen friend encounters on the daily. Shotguns, machineguns, swords, knives, fire weapons, explosives...I could be wrong, but from what I'm seeing on the squirrel's profile, he's seen it all before.
And actually, he has defenses for all of it as well. Body Armour protects him from physical stuff (especially bullets), Fire Armour makes fire/explosive weaponry almost moot against him, Reflective Shots will make any bullets and melee strikes damage Conker instead, and the Death Mask will allow him to simply walk through the squirrel's attacks for a limited time. Cloak of Invisibility is also going to give the little guy trouble if Caleb puts it on, especially since the Voodoo Dolls don't give off any muzzle flashes that would give away his location.
Add that to his hax weapons, better versatility and higher combat skill, and I'd say he takes this quite handily. Not necessarily in a stomp, mind you, but easily enough nonetheless.
Let's be real though, the true ending to this is that they go out, get a drink together and bond over showtunes.
