By looking at the switch. I would bypass it. And do as you suggested. The 120 vac one I posted is much cheaper. But that's up to you. That Hobart is pretty old.
I would remove the old switch gear inside it. And use the enclosure to hook up the new leads. Just nut the wires and tape them. The VFD will give you a bonus of reversing the motor if it jams. Might even be able to add a remote speed control with a start/stop switch if you want to get fancy. Though, I'd need to see the wiring diagram to see if you can do that. Or, a foot switch. Which could be very handy.
I would remove the old switch gear inside it. And use the enclosure to hook up the new leads. Just nut the wires and tape them. The VFD will give you a bonus of reversing the motor if it jams. Might even be able to add a remote speed control with a start/stop switch if you want to get fancy. Though, I'd need to see the wiring diagram to see if you can do that. Or, a foot switch. Which could be very handy.