thank you guys for comments and support
it seems my prelimenary assumptions regarding illuminating evenly the outside cover are fake. More I think about it, more I doubt to make it simple and low cost. So I reconsidered the idea of this power supply.
Mike, I agree. I decided to minimize the lighting area to small part placed at the top of external cover.
Now the question is following: can I trnasport the light form hidden LEDs in the way I described in the picture above?