Sometimes you need to have a way to cut those very small pieces of wood that don't involve your fingers in any way!
This is a small table saw sled I made with a long threaded rod on a toggle clamp. Play around until you get the rod to press down as it also pulls in toward the fence. You might even sharpen the end of the rod or put some sort of rubber tip on it. The two plywood pieces are for setting the length and backing up the cut to prevent chipout. The last image shows my sled stop (red arrow) - just a bolt in a hole in the outfeed table