To handle cactus, take several pieces of newspaper and fold them together into a long, narrow band. That way you can wrap the band around the cactus and have the band to tighten around the cutting while having a handle to move it with. Gloves may or may not help, depending on the spines. I don't use either. For some reason, I am able to handle cactus and not get hurt. I guess it is because I have pricked my fingers so much doing hand sewing that I don't have much feeling left.
I would not cut the piece you have into too small sections.
Be careful with the watering until you see signs of new growth.
For those of you familiar with this particular cactus-would nicking it at regular intervals and just laying in on adequate dirt work instead of cutting it up?
Whatever, I hope you have success with your endeavor.
Beverly A.