It is not a cactus, but a Euphorbia. anoplia to be exact. I would just let the head be.

I will 2nd Zeck's ID of Euphorbia anoplia, common name, Zipper Plant. It is a succulent, but not a cactus.

Now, for the obligatory warning when handling your plant...take care not to get the milky latex/sap on your skin or membranes (nose, eyes, etc.) that may exude from it you bump/poke/cut/break the plant. You may have skin irritation, rash or blisters from the exposure. In other words, if you HAVE to handle it, do so with gloves & watch where the sap goes!

If you want more info/people's on this, you can run a search on this forum.

Enjoy your plant!

Not sure where your from but transition it over the next two -three weeks for some sun

She needs a-lot more big bright sun too they spike off after flowering usually at 90 F better if in the 100s F but use all grits heavy on the pumice
At these temps that soil is going to crash in short bye bye roots
Pic is of a close neighbor and relative E.horrida top in full and more on the way at Avg 108 daily for 8-10 hours