In Sam Raimi's Spider-Man (2002), it's revealed during the class trip scene to Oscorp Labs that the spider that bit Peter Parker is an entirely new species created by combining all the best genetic traits of lab spiders. This spider was just one of 15 super-spiders in the same tank, which escaped for at least long enough to bite Peter.
I don't recall any dialogue about the spider also being radioactive. Was this spider radioactive as well as being a genetic hybrid? If it wasn't at all radioactive, how does the Raimi universe explain Spider-Man gaining powers by being bitten by it?