I don't do power electronics, but I am sure you can power it using something absolutely tiny these days.
My A600 has a "feather brick" PSU and I am sure that with modern switch mode electronics it would be about the size of a packet of cigarettes.
At the very least you'll be able to follow
Keropi's PicoATX PSU mod.
Although I dunno why Keropi didnt just solder off the ATX connector on the PicoPSU rather than build a PCB!?