Just a thought...
Is this shop vac being used as a dust collector when some other piece of equipment switches on?
Check with your local distributor of woodworking tools. Lots of small mom & pop shops, as well as weekend hobbyists like myself use shop vacs for dust collection so there are several companies that make different kinds of remote switches for shop vacs. Some use a remote control so you can start it from across the room (provided you didn't set the remote down somewhere), some use a current relay on the machine tool to start the vac as soon as you turn on the machine. I've seen them advertised and at one woodworking machine supplier here - sorry I can't give you a brand, I still walk across my shop to turn on the shop vac before starting up the table saw or planer, but since my shop is one half of the garage, its not that far.
As far as sizing a contactor goes, use the rated amps of the motor, not the HP rating. Its a single phase motor and you simply cannot rely on anything the motor tells you except its amperage.