New Hampshire seems to be on the 2017 NEC.
The circuit does not require GFCI protection under the 2017 NEC. [The 2020 NEC changes how the "6' from a sink rule" measures distance to no longer stop at doors, so it would require GFCI protection under the 2020 NEC if you use a receptacle.] The disposer should not be on the same circuit as any of the countertop receptacles.
Hardwiring is generically allowed. A disconnect is required within sight of the appliance (meaning within the sink base cabinet, I would say, although some say simply within sight if you are sitting in front of the cabinet), or that is lockable (e.g. the circuit breaker has one of those permanent brackets installed that let you slip a padlock through to lock the breaker off).
Romex is not to be used unprotected where "exposed to physical damage," and there is wide regional variation on how that is interpreted for a garbage disposal. Some jurisdictions have no problem with exposed Romex crossing from the wall to the garbage disposal. Others would say it should be covered with something like smurf tube, while others would require a metallic cable method.
The only way to find out your local practice is to contact a local electrician or building department. Cord and plug connection is always OK and provides the disconnect within site. So on balance I would say that cord and plug connection is a slightly better installation, and certainly one that is not subject to regional interpretation issues.
Cheers, Wayne