"Heck, it could probably even be the Model 53(?) in .22 jet?"
No.
The Model 53 has a very distinct hammer.
The 53 hammer has what appears to be the hollow rivet hole typical of centerfire S&Ws of this period, but it also has separate piece on the rear top of the hammer that is the selector for center/rimfire.
You can see that in these pictures:
https://www.ebay.com/itm/Smith-Wesso...-/184029725073