It goes back to how much you have to cut. If it’s only a couple of small bits, then experiment with various solutions in the way of saws.
If we steer away from thinking of ply as what it isn’t – that is as natural wood – cutting the stuff with hand saws that are specifically designed for cutting natural wood will always end up with a ragged cut-line however careful you are….. and blunt the saws very quickly. Hence, we have hard-point saws that are designed to withstand the vigours of man-made stuff, such as ply and chipboard.
Next, unless the cut-finish is unimportant and out of sight, you’ll end up spending as much time cleaning it up to an acceptable edge as you did on the cut.
Then there’s the problem of plane damage. Good hand planes get scratched to bits and blunt quickly on the brittle glue lines in ply…… this is another tool that is designed for wood, not composite man-made ply. If you want to check what your tools have to deal with, split some ply in half and look at what’s in the middle!
However, there are saws that are designed to deal with this stuff…….. a high-speed circular or table saw with a fine-kerf, 100 teeth at least, they can go to 140 – they are specifically made for this job which hand tools are not. Or a band saw. Third choice is to get your supplier to do it on their machines.
Sorry to cast any doubt on your tools…… but it is definitely a case of horses for courses. You wouldn’t put a race-horse to work with kids riding it on the beach or a donkey in the Derby.
Good luck with it……… you’ll always get a good physical work-out with sheet material what ever you do, but don’t expect it to behave as if it is wood!
P.S. – There was a Paul Sellers work bench made of Birch-Ply a while back. Looking at it again, it is interesting to see that the bulk of cutting the sheet to dimension was done on a band-saw.