Target Disk mode simply turns that computer into an external hard drive, usually connected via Firewire. It will simply appear on the other connected computer as an external drive.
I'm not suggesting that anything be dragged and dropped on to the TD drive. Especially not a MS app. MS doesn't care to operate like any other software company in the world, as far as I know... OK, maybe they trade methods with Adobe... but that's another thread!
All I'm suggesting is that most installers allow you to pick the location where you want to install something. I'm hoping that MS would give at least that option to you.
The set up:
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.
The last option might be to clone the DVDs with Carbon Copy Cloner, if it can do that (despite any copy protection), onto a large enough thumb drive.
Of course, even after all the above machinations, that version of the app(s) may not work in that OS.
As for not wanting to buy a DVD/CD reader, how do you plan on updating the next versions of any MS app(s)? Perhaps they will post their stuff at the Mac App Store? I doubt it... Perhaps they'll have their own version, with an array of virus', trojan horses and assorted malware automatically installed when you visit.
