Should the length of the electrodes in the electrophoresis chamber be proportional to chamber's size?
These instructions for building an electrophoresis chamber don't comment on the minimum length of wire, but on the other hand they suggest using something called Monel Seizing Wire (Ni/Cu alloy - £8.95 for 10 m in the UK) or 20-gauge copper wire, so if you follow their advice you probably don't need to worry about cost. 

I imagine that alloy electrodes won't last as long, but they would be cheap to replace - in fact you would be looking for opportunities to use up all of your excess wire!