In the comics, Billy Butcher doesn't possess powers. He relies on his combat skills, experience, and a never-back-down attitude to fight against those with supernatural abilities.
Well, there are fanfictions where Spiderman gets his powers not from a single spider bite. Instead, he could be exposed to a series of bio - engineered substances that are spider - related. These substances interact with his DNA over time, gradually endowing him with the spider - like abilities we know, such as super strength, agility, and the ability to cling to walls.