A simpler solution than Doug's scrubbing, but you might have luck just brushing or rubbing at your hands and arms prior to cooking, so that any loose hairs can be shaken off before you begin cooking. Hairs seem to shed rather slowly, if all the loose-ish hairs are knocked off prior to cooking I would expect it to be unlikely for there to be more loose enough to fall (without intervention) within the hour or two cooking a dish usually takes.
Alternatively, you might have some luck rubbing oil or cream on your hands and arms a bit before cooking. It would encourage loose hairs to be shaken off before cooking begins, much like brushing, and it may also let your skin stay a bit moister, the better to catch stray hairs or perhaps prevent them from coming loose as quickly.