It would be a rather involved process. The wall behind the valve would have to be cut out to allow access to the valve, the water turned off, the old valve cut ot, the new valve attached to the piping, support framing installed to anchor the valve to, test the installation, and repair the wall. Repairing the wall is a 3+ step process itself.
A good plumber could probably do the job in a few hours, then a drywall repair guy for the patch work, then painting.
Unless the different handle is very important, I would stick with the Moen valve.