Will this phantom power circuit work?
The second schematic is right. The first has polarity the wrong way around and a dead short across the signal lines. You've also got the polarity wrong on the LM386 so be careful!

The Zeners are a good idea. When the circuit is powered up the left side of the capacitors will lift to, maybe, 24 V (depending on the load presented by the mic) and the right side will try to as well. That's the characteristic "thump" you hear on powering up an amplifier with a single supply rail. The Zeners will clamp the signal to a value that won't damage the opamp (but may still offend your ears).

I didn't know if the LM386 could be used in differential mode as you've drawn it. A quick image search for "LM386 differential" shows that others have at least drawn it so you won't be alone in trying!