Ewww i hate spiders too... GROSS!
Do you have a cyclonic vac? If so maybe turn it off, take the bit off that holds all the yuck stuff and run it outside straight to the bin?
I wouldn't spray anything in there as you don't know what affect it will have on your vac... but you can't leave it running ALL day... lol

Hope the gross little bugger gets dizzy and passes out in enough time for it not to move while you relocate it!

GL!