Wrong way to clean a stylus!

First time posting. Have read thousands of comments however. I feel like a complete idiot. I shall explain. I have a Marantz TT-15S1 with the original cartridge without a cover of which the LPs tend to attract dust and dog hair while hanging out between sessions.  There was a tuft of dust/dander on the stylus that I couldn't get off that was creating some serious skips. Dabbed with felt like paper, still there.  Wiped gently with lens cleaning cloth, still there. Got the can of compressed air and tried to blow it off. No luck. Put the straw in the can of compressed air for a more directed shot and wouldn't you know it but the straw flew out of the can like a bullet and took the stylus right off the cartridge. Now, I feel like a complete dumbass and have to spend hundreds on a new cartridge. Thought I would pass along my personal comedy of errors.  Maybe others could discuss theirs so I don't feel so bad?