Shut down the mini.
Have the G4 already running.
Start up the mini by holding the "T" key down.Usually the key is held down until you see the FireWire icon on screen. At that point, there is no longer a need to have a monitor on the mini. However, since you don't normally have a monitor connected to it, just keep the "T" key down until its drive shows up on the G4 (at least in a finder window that has been set to show external drives).
Now, insert the MS DVDs in the G4 and run the installer.
One of the first few screens of the installer should have an option to select different location.If so, select the mini's drive, it should install to the Application folder on the mini by default. You may have to enter the Administrator password for that Mac.
If no, that's not going to work and the disk image may be your only choice short of borrowing a DVD reader/writer. Still, MS is not unlikely to have protection on their installer DVDs and they may not be copyable.