dude! Petrol auto-ignition temperature is arround 250 degreee celcius.....thats 2.5 times the boiling point of water......Im sure friction will not heat up the surface to such high temperatures......... is very much safe to use petrol if there is no naked flame nearby.
The condition of your bike is very similar to the project bike I bought few months back.....I dismantled the parts and for thorough cleaning, I steamed them in a big sauce pan "DEKCHI" to soften the stains and gunk........then used a nylon brush and diesel to make them shine again........ After you clean brushed metal surfaces thoroughly you can get them polished or SAAN as per liking.