Okay, I found this picture on the internet and it depicts exactly the pain those darn spines on a cactus feel like. Pain….So here is what you do about it, and I should know as the last few weekends I have been propagating cacti. For those pesky little glocoides from the prickly pear, or Optuia species I use my favorite duck tape. Yup-slap it on and rip it off. Ouch you say but it goes quick just like a waxing job. I wonder if they use duck tape when waxing-Ha.
Now for those big spines that get under your skin. Well, I hate to tell you but you have to wait it out with them. Hot water seems to help a bit, but really only time gets those suckers out. Eventually they work themselves out.
So your best bet is don’t get em to begin with, but really that is almost impossible working with cactus. I wear leather workers gloves, wrap the cactus in paper bags to transplant, and other than that grin and bear it.