In reply to TobyA:
Somewhere in the hoover, probably near where the cord first enters, there will be a clamp of some type. The clamp grips the cable, and relieves the strain on it, so that when the cable gets pulled it doesn't pull on the solder/crimp/screw terminal which makes the electrical connection. If you do end up cutting and splicing the cable, do it further into the hoover than the clamp. That way, if the cable gets yanked (and it probably will at some point, on a hoover) the strain relief clamp can do it's job. What you really want to avoid is catching the cable on the end of a table, and pulling the splice apart and the cable out of the hoover. That would leave you with a live power cord with bare ends lying at your feet.
Taking the switch apart is good advice, that is likely to be where the end of the power cord is. If that doesn't work and you're left splicing it, then screw terminal strip is a good way of making a connection. You buy strips of 15 or so terminals, and cut off the as many as you need.
Make sure the replacement cord is the right type for a vacuum cleaner. It should be thick enough to carry the current, don't use lighting flex.