There is no especially compelling reason, in most cases, to use hardwarecloth for the whole thing. All you need is to put a smaller mesh material on just the bottom 2-3' of the fence, where reach-through happens.
And indeed if your main run fencing is 2x4 welded wire, you can reasonably-safely get away with a lesser material (if you really insist). If you can find 1/2" poultry mesh (like regular 1" chickenwire only smaller), that is good, or you could even go with 1/2" plastic garden netting or 1" chickenwire if you don't mind it being *slightly* less safe. The thing is, all it's meant to do is keep chicken heads inside, and make it more difficult for raccoons etc to reach their paws in. If, worst case scenario, a predator manages to rip a hole in it, the chicken is unlikely to still be THERE by the time that's accomplished, and the 2x4 wire keeps the predator from entering the run bodily.
JMHO, good luck, have fun,
Pat