I recently wanted to go back to my 3DS after a while of not playing it. Though I found out my dumb self put wrong information for my NNID and Im not able to use anything like the eShop for example. I would delete it however I am afraid it would delete the save files for my games. (The Games are physical not digital)
According to Nintendo, game save data is saved directly to the physical game cartridge. So, deleting anything on your 3DS shouldn't affect the save data stored in the cartridges.
There seems to be some rare exceptions to this rule -- e.g. Super Mario Maker saving both to cartridge and SD card -- but you should be fine deleting your NNID without losing progress data :)
Note: it looks like Pokébank is linked to your NNID, so you may lose any Pokémon you have in the Bank.