Q: network printer

A wireless printer added to your network and the very same printer with an Ethernet connection might as well be two separate printers, as far as your iMac is concerned. You can have both of them configured in System Preferences > Print & Scan, but you have to choose which one you'd like to use each time you print.

If you prefer its Ethernet connection, delete the existing wireless printer entry in Print & Scan and add the "new" printer. You might need to refer to the printer's documentation to determine which connection method it will be using. Not all of them can use both simultaneously.

I think there's some confusion about what you want to do. Try describing your network for us again, please. For example, is the printer a wireless printer and has it joined your network, or are you using "ad hoc" direct wifi from the Macbook Air to the printer?

Are the ethernet ports on the same router/gateway that supports wifi, or is there a second wifi router in the picture?

When you say you can't add the printer, does that mean when the iMac is on ethernet only, the printer doesn't show up in the "default" window of Print & Scan prefs?