Mary - there are two kinds of shears - A guillotine type might work
better for you. There is still the problem of holding down the sheet
so that it doesn’t move, but the better ones do that.
The type you have that has a 2 or 3 inch throat, curves on purpose
so that you can cut circles. Ask Mr Google about guillotine shears.
There is a third choice - a very small band saw from Micro Mark does
a really good job and it costs about $300.