I know that Marvel has said he isn't, heck, his tagline was Greatest non Muntant super hero during the Nineties after all! But, wouldn't it be a fun story for Spidey to figure out he actually is a secret mutant? With his mystic background where he was always destined to be Spider-Man, I think you can consider him a mutant. For the Science background story, I think theres a way he could still be a mutant. Nowadays, radioactivity is used in radiotherapy to cure cancer. Maybe when the radioactive spider bit Peter, it didn't transfer powers, the radioactivity caused mutant genes to kickstart all of a sudden, in a way to help build Peter's body, and immune system.