I suspect that a simple cleaning and a new rebound spring may help with this.
The first thing you should do is purchase the Kunhausen S&W Shop Manual. It's not very expensive and is an invaluable aid in working on any S&W. This is available at Brownell's, Midway, and many other firearms component retailers.
The second must have tool is a Rebound Spring tool, also not very expensive and available at Brownell's and other sources. Frankly, I cannot conceive of trying to install a new rebound spring without this tool.
Then there is the matter of screwdrives of the proper size. Cost for this will range from a low of about 12 bucks to as much as 200 bucks for a full gunsmithing kit with screwdrivers, pin punches, and most any hand tool you might need. Start out with a good basic set, no reason to go whole hog.
Finally, you might want to poke around on Brownell's site and pick up some small parts, such as a rebound spring kit, a mainspring, spare strain screw, and spare sideplate screws. At the same time you should order an Arkansas Stone. BTW, for a rebound spring I would recomend a 14 lbs. spring, it's will lighten both the DA and SA trigger pull a bit but won't cause issues with poor reset.
Once you have your "kit" then it's time to sit down and read up on doing and Action Tuning. It is not at all difficult to do and will only take perhaps an hour the first time you do one. Once your finished you'll have a smoother running lockwork and a bit of pride in your new ability. BTW, I like to keep my mainspring at near factory power. While it won't produce a super light DA trigger, a trigger pull in the 8 to 9 lbs. range is very useable and will reliably ignite any ammo you can find.
Now, tips for your specific issue. First, considering the age a good cleaning is in order. My personal favorite for this task is M Pro 7, smells good and does an excellent job of cleaning up old oils and powder residue. Then re-assemble the lockwork and dry fire the gun slowly with the sideplate off the gun. If that "hitch" is still present you'll probably find that one of the small springs has grown weak with age. The ones I would suspect the most are the hand spring or the spring on the DA Sear. BTW, the DA Sear is a flipping whatsis mounted on the hammer that the trigger presses on during the DA pull. Watch in closely as you cycle the action, if it's not flipping forward as the trigger clears it on the trigger return stroke that may be your problem. Another potential problem is that there may be a trigger stop rod within the rebound spring. I do not know if these were installed in the 50's, however I do know that installing it backwards in my 610-3 caused all sorts of odd trigger freezes. Point the barrel down and it would work perfectly, point the barrel up and the trigger would lock up partway through the stroke. Flipping that rod end for end solved the problem. BTW, this stop rod is NOT actually needed so you can leave it out, however I've found that it reduces buckling of the rebound spring within the bore of the rebound slide and smooths out the DA pull at the very end.
Finally, be careful when working with any springs, such as the rebound spring, they are famous for zinging off into another dimension, probably on top of all those missing socks from your dryer. Also DO NOT force anything and if you get hung up on something, just ask in the Smithing Forum, there are a lot of very knowledgeable folks here who will be glad to help.
PS; one final tip on positioning the hammer block so that you can push the sideplate down with simple thumb pressure. Slide it to the UP position so that it's positioned between the lower flat area on the front of the hammer and the ledge in the frame. If you don't understand this instruction, look for the pic in the Kuhnhausen manual.
