If someone does not have a small table saw to do this sort of work properly then they should look for a safe approach. I would caution everyone that cutting narrow stock where the wood is not completely gripped by the rubbery stuff on the guide rail that they are taking a risk. Doing any machining operation where the stock is not stable and under control is dangerous.
If you have to do it then use a hot glue gun and attach one side (the unwanted side) of your narrow piece to a wider piece of something of the same thickness using a blob of glue every 2 feet.
Peter.