Ick, a tick
Maybe I'm the last one on earth to know about this, but I could have used this advice when I had a tick on my leg a couple of months ago. I yanked it off and spent a couple of weeks freaking out that I didn't get it all out, so I'm passing this on with thanks to Catfish for sending it to me.
How to safely remove a tickThis was written by a nurse, by the way, whom I've found often give better advice than your doctor.
Apply a glob of liquid soap to a cotton ball. Cover the tick with the soap-soaked cotton ball and swab it for a few seconds (15-20), the tick will come out on its own and be stuck to the cotton ball when you lift it away. This technique has worked every time I've used it (and that was frequently), and it's much less traumatic for the patient and easier for me.
Unless someone is allergic to soap, I can't see that this would be damaging in any way. I even had my doctor's wife call me for advice because she had one stuck to her back and she couldn't reach it with tweezers. She used this method and immediately called me back to say, 'It worked!'