I know you wanted a non-chemical reaction - but if you're reasonably sure it's a hair clog, you could try pouring Nair down it and letting it sit overnight, then hot water - that will dissolve the hair. This link (http://www.1800anytyme.com/blog/8-clogged-drain-tips/64/) also has some other tips - I've had both good and bad results with a snake; it depends on where the clog is.
Also, I don't know what kind of drain cover you have - but when my sink clogs, it's usually because of built-up gunk on the drain plug. I unscrew the screw that hold the bottom of the drain plug into the lever that moves it up and down, clean it off, and put it back - and the drain runs clear for months, until the toothpaste gunk builds up again.
Also, if you can find it near you, you can try a high-pressure air or CO2 plunger like this one (http://www.amazon.com/Kleer-Drain-Instant-Opener/dp/B000DZD0VI) - I've never used one, but I've heard mostly good things about them.