I have a couple myself that I need to shaped up a bit. I have done it before and they had no trouble producing new growth lower down on the stems. Al

The only thing I remember about pruning tp's is that when you select the place for your cut above the buds pointing away from the center of plant will grow outward. The buds pointing toward the center will grow stems inward.

If the stem is hollow where you cut you may want to put something in the hole to prevent bugs from making the hollow a home. Wax works or if you have a gum chewer??

You might try sticking the portions you remove in moist soil and place in shade. If you have the touch you will have presents for your friends.