I've never shaved my legs and I certainly never cared if my project won at an engineering fair; since the criteria never included what I considered most important in engineering - innovation, creativity, and brilliance in implementation. It was always - can you make something that somebody else has made work already work too within this time frame, so that you might prove your worthiness to be a productive rat in the maze. The guy who found fire and showed the world how to use it was surely burned at the stake for being different and possessing powers "irrespective" of man.
Shaved, hairy, or whatever the case may be, engineering is not determined by the accomplishments of others but your own. Jack Kilby worked alone in Texas Instruments' lab in 1957 when he invented the integrated circuit. He also failed the entrance exam to MIT. He then went on to head up the team that developed the first hand held calculator at TI.
So shave if you must win the fair, but believe me the real reward will be granted by yourself.