I'm sitting here getting a kick out of "rectifier/converter"... that's funny.
It's called ... a D.C. power supply. ;-)
172 M model... that's old enough it's a 12 volt system still, right?
You'll need a way to connect to the ground power plug. Those plugs aren't cheap, but they are probably the sanest and safest way. I don't know a source. I'm sure they're available though. I forget what they're called.
I believe you'll also find that Cessna disconnects the battery from the circuit when ground power is connected. They close a solenoid.
So make sure your power supply can handle the full load of whatever is turned on, in amps, with some margin, and don't run motors and what not. You'll have no help from the battery or any smoothing via the battery acting as a capacitor. It won't be in-circuit. Check your Cessna electrical diagram for the 172M to be sure, but most had the solenoid in that era.
Jim alluded to the vacuum system. I am assuming this is for "tinkering with the GPS" on the ground, and you don't need the non-electric gyros to spin up. Zero need for that stuff at all. Let us know if you need them, that becomes a whole different thing.
Nice Astron, Brian. The internal design of those is almost stupid-dumb, and there's some better designs out there, but my lord they made a lot of those things. I have an RS-20M and an RS-50A sitting within 15' of me as I type this. I know of an RS-70M that has been in service at nearly full load since 1984. (One of the capacitors has to give, one of these days...)
Now, with all that said, there ARE companies that'll sell you a "special" aviation themed ground power box. You know what's in it?
A D.C. power supply, fed via AC, a crowbar circuit for under-voltage, and high current draw, that disables it and lights an LED until you power it off to reset it.
It'll cost ten times what a D.C. Supply will cost. But it will also keep you from harming things when you hit the flap handle and the supply can't keep up.
The one I've used was in a pretty red powder coated case. They at least gave you that for your extra $700. And the proper connector for a Cessna power port.
Someone at the airport has a fancy powder coated aviation specific little box that also has a slot to shove a Garmin 430 into it. Again, hundreds of extra dollars for doing what Brian has in the photo above. All because it says "aviation" on it.
One final note: On old Cessnas, there's a way for one of the solenoids to fail in such a way that application of power to the ground power plug can backfired the starter solenoid. The ground power plugs are so little used, that it would never be caught ... until you plug in and the starter cranks. Be careful the first time you plug into an old Cessna ground power port, please. They're close to the prop and props being turned by a starter, hurt.