Nope, not a Hudson part in the car at all. The Muntz was originally built by Frank Kurtis' company Kurtis Kraft, in the late 1940s. He sold the tooling to "Mad Man" Muntz in 1948. The car could be had with either a Lincoln or a Cadillac V8. They were built through 1954, and less than 200 were built throughout the production.
You might be thinking about a Hudson Jet, which was a two-door and four-door sedan built in 1953 and 1954. The Hudson Italia, of which 24 were built in Italy, was built on a Hudson Jet chassis and have the same engine and trans (202 ci Six with a manual or automatic trans).
Top to bottom - Muntz Jet, Hudson Italia, Hudson Jet
Note the shift quadrant is for a GM Dual-Range Hydromatic. The shifter collar does bear a resemblance to a late '60s - early '70s Mopar, but it's not. Note the lack of Park.
I had an old Muntz 8-track tape player that mounted underdash. Had that in a '66 Mustang when I was 16, then ditched that for a Realistic cassette player.