"I don't have access to a Mac with that older OS. Can I install it on my mac temporarily?"
Sorry, but no. Unfortunately, we are in the extremely difficult stage that I mentioned earlier.
The first obstacle to overcome is that the firmware on the AirPort Extreme must be updated so that it will work with the Mac that you have.
But, you have to use an older Mac to update the firmware.......which should have been done 6-7 years ago.
Kind of a Catch 22. Maybe you have friend with a PC who would be willing to download and install AirPort Utility for Windows and let you use the PC for an hour or so?
If you are near an Apple Store, maybe they could update the firmware on the AirPort Extreme for you?