It sounds like your printer creates a small wi-fi network so devices can connect with it. It's not uncommon. Somehow or other your iPad decided that the printer's network was the primary network, so it connects to that by preference.
Forgetting the printer's network will stop the iPad from automatically connecting to it. But, if connecting to the printer directly (using a printing app) was how you normally print, then that feature will go away unless you add the printer again. If you know how to re-add the printer, it should not be a problem. The iPad usually picks networks by when they were added. First come, first found, so re-adding the printer should make it the second choice.
If you don't use a printing app and the printer's wi-fi to print, then deleting the printer's conneciton from the iPad shouldn't be a problem.
Reseting the all network settings shouldn't be necessary unless deleting the printer network alone does not work.
Even if deleting the printer alone works, you should still find out what your wi-fi password is and keep it in a safe place. You never know when it might be necessary.