You can go with mITX and get a mITX case designed for an external power supply. I might be sending you down a rabbit hole but you can get what are called PICO power supplies.
A big trap about these is they are often 12volt input only, there are versions with multiple input voltages which makes them great for recycling old laptop chargers.
This is how I manged to get a 65 watt FM2+ APU into this case for my nephew. Its not silent but but Arctic has a nifty looking passive cooler called Alpine AM4 (AM2,3 4 and FM1 and FM2 all share the same mounting system) I would have gotten if I saw it in stock.
Check out a site like Mini-Box.com if you want to chase the white rabbit.