Bit late in the day for this now but I've hotswapped with Xboxes before.
Unplug the DVD lead from the stock one and boot up a modded one with a boot disc with FTP support, or maybe a file manager.
Once booted, swap the IDE cables so the modchipped cable goes to the stock HDD. You can now FTP onto the stock HDD. File manager seems a bit hit 'n' miss but that is to be expected.
I can't recommend the practice when there are better alternative methods.
Obviously it's not time saving if you don't have both the case tops off