Was it a smelly spider? Just wondering about the deoderant..
As I said, I went all Macguyver. I made a siesta-powered taser

But seriously, deodorant makes them all dizzy and they run away, like bug spray but weaker. It eventually fell off the wall after I sprayed it with the deodorant and poked it with the coathanger, so I trapped it in the sombrero

so we just need these three items to get rid of spiders in Skyrim. If we can trap that giant spider and put it outside it'll be ok.