Why not do a catch,measure and release? Use a length/weight chart. Fish could be measured,recorded and released at boat,or measured and released at 'weigh-in'. No scale would be necessary.
It might not be as precise as weighing,given thick vs. thin fish,but it would be fair. If it's a 'small' event,it wouldn't take long. You just need a calculator,weight/length chart, and a 'golden rule'.