I assume you have gotten to the point where you have chopped the lead of the AT Power supply and connected to the A1200 connector.
Now once you have done that you can either:-
Splice the floppy connector to power the hardrive.
I would recommend this method as putting too much load on the floppy connector can lead to tracks burning out as they are very thin.
Take the motherboard out of the A1200 turn it over using a multimeter find out the voltage on the pads where the power connector is soldered.
For Hard Discs / CD-Roms you need +5v GND +12v
Cut one of the D-connects of your AT Power Supply with plenty of wire, as close as to the Power supply as possible.
Solder the Yellow (+12V) to the +12v Pad
Solder the Black (GND) to the GND Pad
Solder the Red (+5V) to the +12v Pad
Obviously verify the colours and voltages using the multimeter on the AT power supply first.
This way the load you require is not being drawn through the motherboard.
If you are feeling confident you can solder directly on the back of the Power Connector in the A1200.