I would say you are right about the long exposure. Some flashes have a strobe function. You can set the number of flashes and the speed at which they fire.
I guess if your background doesnt have any features, dark sky etc., then nothing will happen to the film until the skater goes over it and gets flashed.
The other way to do it would be shooting a sequence multi exposure. You do need a fancy camera though for that, and a bit of math to figure out your ambient light exposure, since your going to expose it as many times as you have frames in the sequence.