Whilst I can’t help a great deal I would hazard a guess at this being late 40s / early 50s
Hamilton in this era were a very good watch maker, it’s likely to have a quality movement inside. I think it is well worth getting up and running, not sure the dial would clean up much but it’s looks like it could be a redial - sorry reprinted dial (just in case we get some members getting in to a hissy fit again), the Hamilton logo is not centred on the 12 and the minute track is way off.
The styling is very much of their time, think Cadillacs with fins and rocket intakes etc. I think they are cool.
It’s a nice find.