Buzzing and leaking sprinkler valve
"Should I just replace the entire valve and assume the wiring is
good?"


Don't assume, you should test the wiring by connecting the wires from the problem valve to the valve next to it and activating that station using the Manual feature on your timer (or waiting for it to operate according to your existing timer schedule.


"Should I just replace the entire valve and assume the wiring is good?"


We can't tell where the leak is coming from so we don't know if it needs to be replaced, maybe it just needs a simple washer or o-ring. Most valves can be rebuilt using a washer/gasket kit (those are particular to brand and model, get the info off of the valve and google it). The solenoid can also be easily replaced (the buzzing noise, whether it still works or not, may be an indicator of near-future failure).

I don't mention rebuilding as a money saving strategy, I mention it as part of the answer to your second question:


"is there a way to get this off without cutting the pipe?"


NO