I'm gonna go ahead and recommend the F3 as well. I've done a handful of shows now with it and for me it's a bit of a game changer. Your money is definitely better spent on your mics and Neumann KM184's are a great choice. I think we sometimes forget that the cardioid polar pattern is probably the most flexible polar pattern and you can make great recording after great recording regardless of the situation.
My tests with my F3 indicate just over 3 hours with standard Amazon rechargeable AA's. I've read people are getting just over 3.5 hours with the higher capacity Eneloop (?) rechargeable AA's. I haven't tried Lithium's but yes, they should get more than the rechargeable options.
I grabbed this 2 pack of portable cell chargers off Amazon and I've recorded 5+ hours without even losing a single light on the charge indicator. They are tiny. I also grabbed a right angle usb C to usb A cable to go with these.
https://tinyurl.com/yvp7jjnzIf you are set on KM184's, using an M10 as your recorder doesn't make sense unless you want the flexibility of stealth recording with it. Then, as everyone has mentioned, you would need an external preamp with phantom power like a Shure Fp24, Sound Devices Mixpre D or MP-2 to run in between your mics and the M10. There are plenty of external preamps that supply 48v out there, others can chime in.
There are plenty of older (and now cheap) all-in-one recorer/preamps from Tascam, Marantz, and Zoom. Those would sound just fine with KM184's in my opinion. Sound Devices and the newer Zoom models are really nice all-in-one boxes and if you have the money you can't go wrong with those.