The axle nut is indeed regular thread. I’ve used the vice trick before, as well as a pipe wrench to get stubborn axle nuts loose.
Edit: to clarify, are you just using the vice to hold the wheel upright? You can actually turn the wheel sideways and clamp the smooth end in the vice, then crank on the nut. Or hold the wheel upright and use a pipe wrench on the smooth end, and socket on the nut. Some heat will help.