That’s what I would do...electric fencing would likely cost under $100...Enclosing a run of that size with hardware cloth is going to cost an arm and a leg. How many birds? What is the size of your coops?
A cheaper alternative might be to use chicken wire, and put bird netting over the top (if you are not in snow country) then run electric fencing around the perimeter. This will keep out all but weasels.
Only you are in touch with your risk tolerance as it relates to your finances.