It shouldn't be difficult. Maybe a photo of your wireless door bell will be good.
You can also buy a wireless remote control, which will definitely solve your problem.
Of course it is possible.
There are many example in our nature environment.
Sunlight is a form of wireless power transmission.
Power from the Sun, solar panel at the receiving end.
Wind is also another form.
Alternative you can just tin the high current copper trace path to make the trace thicker.
Try to make the path as board as possible.
Not all path need to be so thick. The PCB board can be very expensive.
You can also try to approach PIC-CONTROL for a solution.