That could actually be a fun build. Like, if paws gave you 1-2 damage per STR instead of the base 1 per STR that unarmed normally has. Way less than what a weapon will give you, but you can never lose access to them.
i mean you could add pads to the hands too, don't think it'd matter it it assumes fingers, as they would still be fingers, just they would have pads¯\_(ツ)_/¯