I spent a few months living in a very heavily tick populated area, and removing ticks from dogs and people was a daily thing, I must have taken 10 or more out of my own legs and groin. We never used anything more advanced than tweezers but these are risky. The main worry is lymes disease, which I'm told can be chronic and really mess people up, though its not officially recognised everywhere as a cause. If the tick is found when it first bits and is removed clean the chance of catching lymes are very slim, even if they do have it to pass on. Apparently the biggest risk is leaving them in to suck away, or pulling them apart and leaving the head under the skin.
I found that removing ones from dogs that have swelled up is quite easy as long as you pinch it just right, not too hard, not too loose, twist it 400 degrees around anti-clockwise (i think, can't remember...!) before pulling very gently then you hear the 'tick' signalling a clean removal. then burn the little sucker.
I found my folks' cat with tics all over the ears and used neem oil on them rather than fall out with the cat by tweezering all the tiny things off its face. Neem oil works a treat. It is totally non toxic to all creatures great and small, besides those creatures which are both insects and bloodsuckers/biters. Bloodsucking parasites forget everything they are doing when in contact with even the smallest trace of neem oil. They forget to eat, drink, defecate, mate or even hold on to the skin of the host.
I checked the cat an hour after smearing a tiny speck of neem oil on its ears and every tick had vanished.
Neem does stink, but is effective in very small concentrations. Next time I'm in a tick rich area I will have that stuff smeared on my belt and boots, and make sure dogs get a bit rubbed into their undersides. After seeing how it worked on the cat I think you can't go wrong.