You want to change NES emulator/core, or any emulator/core change...
Select NES from wheel or button, now you see your NES games in view with art correct?
Click home button on Wiimote, now click Select Plugins. You need to scroll until you find "Nintendo NES (Nestopia-RA) and check mark the box. The FCEUmm-RA box needs to be un-checked.
Now press the B button a few times until you are back at the game screen, where your art is displayed. Press the Home button on Wiimote and click "Reload Cache".
In my experience, i usually start another game from a different system, where the cache has already been set, then exit quickly. This way, i know the settings should be saved, in fact, this is a rule i abide by each session.
Now, Nestopia should be your NES emulator and it has come a very long way over the past year, as for how well it performs in all aspects of emulation on the Wii.
I would say it is as good as FCEUmm now and that is saying something. FCEUmm is a great emulator.
As an avid NES & Sega Genesis player, which are the 2 most underappreciated libraries in the history of gaming. The Wii performs as well as any PC using emulation. If you are using a NES emulator on the Wii, you must be using FCEUTX, if you are not, fix this issue!