No Battery Microcontroller Operation - (Motion, heat, induction etc)
10mA is quite a lot for a coin cell. And of course the duration is really low.

As for wireless power transmission, I highly discourage you. Since you are using coin cell batteries I think that size is a must for you, and for wireless power you will need a really big antenna. If it is a wearable I think that the receiver is on the body too, and so much power is not a good thing.

In my opinion and according to my experience you have two possibilities:


use alkaline batteries (e.g. AAA). Use a step up driver to get 3.3V from 1.5V (since the current you need is low you can use simple charge pump regulators, so with a 10pin TSSOP integrate and three small capacitors you are done) and you will get a really long lasting circuit. Drawback: AAA batteries are a bit large, so probably you'll have to make a bigger receiver
use lithium batteries (usually I use LiPo). You will then be able to recharge the battery with any power supply (I usually use an IC which can charge LiPos with a 5V source - USB - and a couple of other components (two capacitors and a LED with its resistor).


Personally I struggled with coin cells for a long time before giving up and sticking with lipos forever.