Ive had a coupla teeth pulled. I just wet a tea bag and chomp on it over the tooth hole and smoke away. No problems. They say that nicotine causes all kinds of healing issues but I haven't found that to be the case with me. The coffee is fine as long as it's lukewarm. You don't want anything hot dissolving the blood clot. After a week I stop using the tea bag, once the extraction site has firmed up a bit. The tannins in the tea help stem bleeding and soothe the site, too.
They're warning you about dry socket, which is terrible. It's truly the most painful thing I've ever experienced, and I've papercut the webs between my fingers, so I know. Here's how you get dry socket: eat chips and dip the night after an extraction. That'll pull the blood clot right out. Clove oil on a Qtip does wonders.
Im not a doctor or dentist, but I do perform shade tree dentistry and amputation, pretty cheap.