I agree that you should not do judging. It takes a lot of volunteer judges, it takes more time than you think it will, and someone always gets upset. Skip any formal judging and keep it casual. The show will be better without it.
Maybe make the people's choice award something desirable but only cars that register and pay a nominal entry fee ($5?) are eligible. That way the show is open to everyone but if you want a prize you have to register and pay a little. Maybe the prize is a trophy plus something useful like a meal at your Cafe or some donated item of some value.