probably not gonna happen ...
If you can remove the switch and post a photo of it, we can compare it to other switches of various types. A saw that old will not have a parts supply obviously.
In the event you can not find a switch that will fit inside the handle there are other ways to operate the saw in a safe manner. If you were to wire those 2 leads together, the saw would be "permanently" ON. You could then add a remote switch, like in a power strip, into which you would plug the saw. Then the power strip switch would become the ON/OFF for the saw. I prefer the switch as close to the handle as possible on my RAS for safety and ease of operation.
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)