My table saw stand is full of different push sticks for safely guiding wood through the blade. One of my favorites is the MicroJig that Tyla picked up for my birthday. It is easily configurable to handle a lot of different situations and it really protects my hand.
If you don’t want to shell out the money, the other one that I grab often is probably something you can build for free out of scrap wood. It holds the piece down well and has a replaceable stub of wood on the back to help guide the wood through. And it doesn’t matter if the blade cuts into your push stick. It’s just scrap wood so you can easily build another one at some point. Jay Bates has a good video about how to build one: http://jayscustomcreations.com/2014/03/the-best-push-stick-ever-invented/