obviously, the "WiiU Widescreen" option is for ... WiiU only.
There's no way to force a real 4:3 output from the loader's setting on Wii, you need to edit your setting in both the console and your tv!*
- Wii setting > video > output > 4:3
- TV Setting > set your output to 4:3 to force the black bar on the side.
now you have the proper resolution for 4:3 games.
But you should know that some games are compatible with 16:9 (windwaker, starfox, etc.), and you'll have to do the reverse setting to get full screen.
On WiiU, it's easier as there's just a single option inside the loader (wiiu widescreen option) to add the black bars on the side without editing the TV or wiiu setting.
*in fact, the Wii does not output widescreen. it's always the same resolution for both 4:3 and 16:9 games. Nintendo did a really poor job in 2006. (probably because widescreen tv wasn't widely used and lot of CTR still used?)
the TV does not get information about the ratio, so you have to set your TV setting manually.
When you play a Wii game, the console tell the game to do the work on the screen buffer to enlarge or skew the picture to fit in the same output pixel resolution.
if you set widescreen to your wii settings, it compress the picture and remove some information (vertical lines) to fake a wider view and remove distortion when displaying 4:3 on a widescreen tv.
When you play a gamecube game, the game is not affecting the picture buffer (it wasn't part of the console's spec on gamecube) and the display (being 4:3 or 16:9) always take the full tv area without compensating the TV ratio.
Nintendont added a setting to "enlarge the game view" and fit more picture data in the same area (this is what wii games are doing when you set widescreen in the console's video setting) : enable "force widescreen" option.
some games will look bad (like Paper mario) as the part external to the screen is now rendered on screen and it was never meant to be watched by the player.
So, you have few choices :
1. enable "force widescreen" nintendont setting : compress the video buffer to display a larger area in the memory (removing some pixels on screen), which will be stretched by the TV and the resolution/ratio will be good for most games. some games will look bad.
2. set 4:3 to both your Wii and TV : you'll get the native resolution, with black bar on the screen's side.
3. play on WiiU and set "wiiu widescreen" nintendont setting : Replaces option 2 without the need to edit hardware settings.
A counter part of using WiiU is that the the WiiU is adding an overscan all over the screen in vWii mode, adding black bars to the picture and making the gamecube game ratio a little compressed.
Nintendont has a setting to edit the picture ratio and position.
video modes on Nintendo console are a real nightmare