Cosmic Spider Man will full knowledge of how to use the uni-force, and well at max power with the intent to kill King Thor with no remorse or mercy and as fast and quick as he can.
King Thor with Odin force, Mjolnir, bloodfrenzied, runes of asgard fighting against Cosmic Spider Man.
Thor with the odinforce, knowledge how to use it, and the ancient asguardian runes = Lord Thor
Thor with the odinforce = King Thor
Anyway back to the battle, "King Thor" wouldn't know how to use the runes, or his odinforce fully. Cosmic Spiderman has a good chance, but most likely King Thor.
This is a tough battle, but your rules go against the very nature of Spider-Man. Even with the Uni-power, he didn't ever have the urge to kill, that's not his style. I'd go with King Thor, but it'd be a tough battle.
He still wouldn't kill him. He didn't kill Carnage even after he murdered dozens and dozens of people during the Maximum Carnage storyline. He won't kill Green Goblin even though he killed his girlfriend, his best friend, and his clone 'brother.' Spider-Man doesn't kill, ever. Besides, King Thor still has the edge here.