The guage of the wire doesn't matter. Guage only matters when you start thinking about how much current you are trying to carry, ie battery to starter = big wire (low gauge number like 2 awg), common circuitry wire where loads are not large = smaller wire (higher gauge number like 18 awg).
As far as wiring diagrams, you might go to the snapper website and click the manuals link and enter your model number in the box and see what you get. I have noticed lately that they do not support their older models like they used to. Several years ago, I downloaded my manuals from there but now none of the manuals for any of my mowers are listed anymore. If the website doesn't do you any good, I guess you will be looking for someone on here that has one and would be gracious enought to make a copy or your looking on ebay.
With that said, magnetos are not extravagent in their wiring. The big wires go to the plugs, the little wire is the ground lead, that's it. Unless you have something I have not seen before......I haven't looked to see what a 1642 is but I have a RER that had the 8hp motor on and when it self destructed, I put on a 13.5hp and it still only had a spark plug wire and a ground.
Just thinking a little, sometimes the alternator wire (mine is dark blue) and the mag ground (mine is black) can be confused, and then there could be an extra wire off the engine alternator for headlights (mine is white) and because the mower isn't equipped with headlights I just capped it off with a wire nut and put that in my brain as "for future expansion" , so physically tracing wires back to the source is always a good thing.