You could use a PC style power box to power the whole system but you'd have to make an adapter for it using instructions on
this illustration (I think). Also it would have to be an AT form factor power supply becuase ATX ones have a different way of switching on and off.
I'd recommend against running the standard power supply that came with the A1200 as it is only a 25 Watt supply. An A500 power supply is at least 35 Watts so maybe running an A500 power supply and using a power connector splitter on the floppy drive power connector might work. The problem with this method is that, in addition to all of the cables that come trailing out of the case, there is the issue of the amount of power the trace leads on the motherboard can handle.
Maybe somebody can find a better description of how to make the PC power supply to work on an A1200 than I can.