Certified GKH Gardening Expert
Yes, this will be ok. Just start with the top tallest leaders. After they show new growth after the cut, then you can cut the others in the same manner. This will often force it to grow bushier as well.
This article will give you more information on the plant: https://www.gardeningknowhow.com/houseplants/crown-of-thorns/crown-of-thorns-houseplant.htm