Saw blades are attached to the handle with rivets or screws, with “split nuts” seen on most “quality” saws. An example is seen in the right of the photo. These are cast brass, embossed “Pat. Dec. 31, 1867”, from a J. D. Darlington backsaw. These are quite nice, some older British ones I have are very crude. Either way, I find them a royal pain in the butt to use (and I have a split nut driver). They are thin, the blade cuts them quite nicely if they loosen, the threads are shallow and strip, the slots are too shallow to grip the screw driver and get chewed up. I usually have to make replacements when rehabing an old backsaw. So, they were something I didn’t want to copy.
The countersunk washer keeps the screw head from biting into the wood handle (and the wood from “growing” over the screw head, another problem split nuts have). Lee Valley makes these in brass or stainless steel (Lee Valley Countersunk Washers, 01K70.51) or you can make them with a 82 degree counter sink (the aluminum one at the center back). The #10 washer is 7/16” in diameter, which is close to split nut size. For the nut, I make a tee nut (7/16” x 1/8” head, 1/4” shank x ~5/16’” overall length, depending on handle thickness). As things never quite line up, the nut binds in its pilot hole (during assembly) and doesn’t turn, so I don’t need a lock washer or square shank. The nuts with a through hole are easy to make from rod stock (assuming you have a metal lathe), the closed ones are a pain. My bottoming tap doesn’t cut as close to the bottom as I’d like so I made these from two pieces: a short length of 1/4” rod (with a threaded through hole), a cap with a blind 1/4” hole (I bored the end of a rod (on the lathe) with a 1/4” [center cutting] endmill chunked in the drill chuck). The two were silver brazed (as in real silver solder, 56%, melts at 1200 degrees, very strong) together and post machined (brazing causes things to move and change shape). You have to think the through hole is really ugly for this to be worth the effort. If you care, I think a better/easier idea is just use a long screws, assemble, cut the screw and file flush (which is what is done with split nuts, which stinks because as the wood shrinks, you tighten and the threads protrude. As they do on all my old saws). For another take on this, see the Norse Woodsmith’s Poor Boy Split Nuts.