Wireless charging seems to be a good solution for your problem, but you should notice that if the primary side of the converter is located near an aluminum or metal piece (like some window frames) the efficiency might drop significantly as it will also induce currents in those pieces.
If you want an off-the-shelf solution, in the past some manufacturers provided wireless charging solutions for mobile phones that didn’t include that feature (they might still make them nowadays). As the secondary side provided a microusb or a similar conector for charging the phone, it might work with your camera.
On the other hand, if you prefer a DIY solution a 2 step converter might be easier to implement, as it will allow you to use a DCX converter or a low bandwidth loop at the wireless stage, avoiding the need of high speed wireless communication channel to send the measured output voltage from the secondary side back to the regulator (wireless converters usually produce interferences in nearby antennas if they aren’t correctly shielded). Additionally, I would recommend you using PCB inductors for this stage as they are usually easier to manufacture
Regarding the voltage, using higher voltages allows to have smaller currents in the inductor which is a nice thing for reducing power losses, yet it is not critical for such a small power application. I would choose it high enough to be sure that the secondary stage can be implemented with a buck converter, but small enough to use low voltage rated components