You are setting the firmware in the Airport Express. It makes absolutely no difference whatsoever which machine you run Airport Utility on. There is one caveat which is Airport Utility allows you to save the setup for any and all Airport devices in a file on the computer you are running Airport Utility from. To expert or import a configuration file
  1. Open Airport Utility
  2. Select the device you want to save the configuration file from
  3. Click on "Manual Setup"
  4. On the menu bar go to FIle > Export Configuration File


If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein