I second that, Al. Scott, check out the razor saws. You should see a selection similar to what you'd find for woodworking saws, that is, you can get saws with different numbers of teeth, for finer or rougher cuts. I have 3, though I think 2 of them are the same model, just with different model numbers. I use a #35, which has a medium blade, and a 230, which has a finer cut, with more teeth. I also have a #235, but it looks like the #35, and since I bought the #35 over 30 years ago, I expect it's the same blade. Either blade will give you a relatively fine cut, with a small kerf.
The blades have a back made of a piece of folded sheet steel, which is shaped at one end to fit into a handle. I tend to hold mine by the back of the saw, though for some cutting, I do mount it in the handle. The handle also fits some other blades, like a #2 hobby knife blade.
There are other makers besides X-Acto, but the design is pretty much the same, regardless of the maker.
Hope that helps, prosit!
Brad