I haven't tried it, but for an Iyonix you could probably get away with using a PicoPSU ([link]) in combination with a laptop power adapter. I think an Iyonix is likely to consume 50 to 70W in general usage (disclaimer: I've not bothered to test this). Therefore a 120W PicoPSU would seem easily well specced enough. You should be able to pick up a PicoPSU & suitable laptop power brick for about 50 quid.
For a typical X86 desktop PC though, it's just not likely to provide enough power to cope with peak loads. The only fanless ATX PSUs I've managed to track down above 200W all cost 90 quid or more, and that put me off.