I expect it will work just fine going from the CA mics > 9200 > Apogee. Going unbalanced > balanced is ideally done with transformers, but people do it all the time without them, and I expect you will be OK too. I don't predict it will sound better than the M10, but I don't predict it will be worse either.
Yes, you need something for plug-in-power, and the 9200 will do that just fine. You could use a battery box to power the mics and add the gain with the apogee pres, but I'm not sure if that is "better"... it may have a different flavor, which you might see as an improvement, or you might not. Gear testing is why god invented opening acts. :-) Try a few songs with the Apogee gain turned down and the 9200 gain cranked, and then try it the other way... 9200 gain turned down to 0, and Apogee gain cranked.
I wouldn't overthink the cabling aspect. The mics > 9200 are all figured out by Chris, and I'm sure he thought about it carefully. Find a typical 1/8" mini plug to RCA Y-cable which you probably have, and some RCA-1/4" TS adapters to plug into the Apogee.
If that were my setup, I think I would use the CA mics > 9200 > m10 for AUD and Apogee for hot board feeds.