If you had to choose.... which trees would you eat?
I think either chicken wire or hardware cloth would work. I can't imagine chewing on wire is pleasant. It'll probably be easier than building fences too. Either way, now that you know it shouldn't be really difficult to control as beavers don't climb or jump. I would only suggest not making the same mistake I did with some birches. I wrapped the chicken wire right against the trunk and it grew right into the wire. It's stuck there now. Stake around the tree and apply mesh to the stakes.