What doctor/specialty can order conduction test for neuropathy?

Any specialty. Any physician (md or do) or podiatrist can order. The test itself should be performed by a physiatrist (physical medicine and rehabilitation physician) or neurologist.
See below. Any medical physician (md or do) can 'order' an EMG or nerve conduction study. This is done by consulting a physician skilled in performance of emg/ncs, usually a neurologist or physiatrist (pm&r physician). Look for someone who is board-certified by the abem (american board of electrodiagnostic medicine) or has additional training (fellowship in electrophysiology or neuromuscular medicine).