It will itch, swell, inflame and irritate, but yes, you can hack it, unless, God forbid, you’re anaphylactic. Do you have any honey on hand? A dab (covered with a bandage to keep it from getting all over other surfaces etc) on the sting site may help draw out the pain. Use a credit card or something similar to scrape the stinger off the site. There’s another trick (I forget what) to relate that helps…
Discussion
When I picked the thistle out of my leg... oh, that's a bee... the stinger somehow came out. I might even have squeezed the venom into me because I thought it was a prickly leaf of some kind before I noticed it was a bee.
10 minutes it in was really "stinging", but right now I can't even feel where it was.