BTX is a dead horse I think the only BTX boards you'll find still around are P965 or P945.
The switch only needs to be any momentary switch like a door bell switch.
If you run a USB hub on your desk the receiver of the keyboard /mouse can go there or run the receiver wire through the wall and plug in directly.
The Antec 900 is good for cooling as is the CoolerMaster Cosmos but pricey.
Or the CoolerMaster HAF, probably a good idea to vent the closet somehow otherwise you'll just circulate hot air in the case.
Another way to think about this (out side the box
) is why do you need a case? I have an old P90 mounted to the bottom of a HO train platform works fine, with a newer system you'll need to add a fan to blow over the motherboard and of course a decent CPU cooler but without the case the components are not confined so air circulation is naturally better.