I am with Nick. No way I am shutting it down or shutting the fuel and the engine unless I see really big flames or I am feeling very warm. I have a fire extinguisher and I can jump out in a second and put it out or at least grab the camera for a final picture. Although certainly US specific, single engines in the US are typically about 500 - 700 feet and you can get to the ground in seconds with power on. Why risk a power off auto when in reality, most true engine off autos in a real situation end up in bent aircraft which has a higher chance of bent or broken body parts on people.
The nose is the best instinct and as a second indication, I have my hook mirror turned to the aft so in the event I smell something, I can look into it and try to see smoke or the glow of flames. Although there are no statistics, my bet is that most times when we smell smoke it is some form of electrical smoldering or the burning of a lubricant and not a true fuel fire. I am not going to raise the risk parameter by shutting down unless I am fairly convinced the source of flame, smoke or smell is actually fuel.
I have had a situation where there was a smell of something burning. Landed quickly and it was a leak in a cooling line to the main rotor gear box. Tons of smoke. Shut down, made the call and waited for a mechanic. Worst part was a Robinson brought the mechanic and the part and the driver handed me a sales brochure for a new R44.......
What I love about the R22 POH is that in the event of fire it tells you to put the fire out with a blanket or dirt. How many people carry a fire retardent blanket in their R22?