Question for Plastic Canvas Crafters About "Nubbies"

Most of you know that I usually crochet, but there are some plastic canvas projects I also make. When I make my plastic canvas and satin ribbon crosses, I have no problem with what I call "nubbies" because the edges are left ragged and uncut.

However, when I make the cross-in-my-pocket items or magnets or anything else, I go crazy with the "nubbies."

"Nubbies" are what I call the little smidgeons of pieces on the sides of the pieces of canvas. Most times, I cut them off while leaning forward over a little trash basket. Even then, there are sure to be a few (or a few dozen) of those little poppy-seed size pieces of plastic that fly onto the carpet. I am forever using the carpet sweeper to get them up so that they do not get into Tigger's fur. Plastic, no matter what size, in a pet's belly, turns as hard as glass and is as damaging. Even without the beloved cat, walking in one's bare feet over those "nubbies" is not pleasant.

So, my question:

How do each of YOU deal with the "nubbies"?

I do not have enough room, at present, to lay pieces flat and slice with a crafter's knife or tool, so that's out for now. I cannot wait for some practical, realistic replies.