Shut down as per the POH but I believe slipping away from the flames can be a good Idea fire walls don't hold up for ever
The standard:
Sec. 23.1191
Firewalls.
(a) Each engine, auxiliary power unit, fuel burning heater, and other combustion equipment must be isolated from the rest of the airplane by firewalls, shrouds, or equivalent means.
[(b) Each firewall or shroud must be constructed so that no hazardous quantity of liquid, gas, or flame can pass from the compartment created by the firewall or shroud to other parts of the airplane.]
(c) Each opening in the firewall or shroud must be sealed with close fitting, fireproof grommets, bushings, or firewall fittings.
(d) Removed and Reserved.
(e) Each firewall and shroud must be fireproof and protected against corrosion.
(f) Compliance with the criteria for fireproof materials or components must be shown as follows:
(1) The flame to which the materials or components are subjected must be 2,000 ±150° F.
(2) Sheet materials approximately 10 inches square must be subjected to the flame from a suitable burner.
(3) The flame must be large enough to maintain the required test temperature over an area approximately five inches square.
(g) Firewall materials and fittings must resist flame penetration for at least 15 minutes. .....................
So you should be okay for 15 minutes, according to the standard. If there's a pilot who can glide a 172 from a normal cruising altitude for more than 15 minutes, I want to fly with them, they would be an excellent power off pilot!
Humour aside, in the very remote chance of a fire in the engine compartment in a 172, turn the fuel off, and the hazard will be very greatly reduced. Engine oil is a very small risk. Now, for a turbocharged plane, the risks are increase a little. If a fire has been caused by turbo scavenge oil being blown onto the exhaust, that's bad. Then, yes, shut the engine down IAW POH procedures. I agree that stopping the engine will stop oil pumping, though a windmilling engine pumps much less oil internally. But, if the engine oil is being pumped into a fire, and you've shut it down, it may seize before too long, and then it certainly won't be pumping oil any more!