How do I print to a NON wiFi printer from my laptop to a printer connected to a desktop computer?

Do this: on the computer that is directly connected to the Printer, modify the Printer sharing settings until "Everyone" is allowed to share that Printer.

then try to add that printer on the remote computer anew.

Why not allow "everyone" access to that printer, then you don't have issues with usernames and dialog boxes when you attempt to print.

Now on the Mac from which you want to print, you need to add-a-printer, and create a local print queue for the Printer you have shared (made available for use). Iits name should now appear in the list of available Printers.

have you changed printer sharing on the Mac that is directly connected to the printer to allow EVERYONE to print?