Never ever, don't ever pinch the work past the blade.
If the blade and fence are truly parallel AND the work is not harboring tension, then everything will work properly.
When I'm 'shaving' the edge, I'll use my thin ripping jig I showed you last week on another thread. And for short pieces you mention; if I didn't have my jig, I'd use one of my Grripers. However, since it takes me longer to adjust the Grripper than the jig...the jig is my first choice.
Short stock and thin pieces cause the most tablesaw accidents....Be careful and if you have the slighest doubt....don't do it!
If you need a step by step on the jig, just ask.....Joe
Built one Joe's thin strip jigs at one of his workshops a few years back. You are welcome to come over and take a look if you like.
Wayne