No, the shrink tubing at the end of the rope is just for identification purposes and does not hold the rope together. If you want to cut your rope shorter without tying a tail knot, you will need just a few things: tape to hold the rope from fraying, a sharp blade, and some type of heat to seal the rope shut again.
Wrap the tape around the spot in the rope that you want to cut. Then, using a sharp blade (sharp pruning shears work well) cut through the tape. Lastly, use a heat gun, lighter, branding iron – anything with a good amount of heat – to melt the fibers of the rope. This is what holds it together so get a good amount melted to ensure the strands will stick together.