Profiles can't be disconnected from a console. However if a mod sees that that friend code is connected to dozens of consoles it is very unlikely that that mod would ban all consoles that have ever used this friend code. Just hide it using the wiimmfi portal and make a new one, it is highly unlikely that your console gets banned for something someone else does on another console just because they share a friend code.

Also, it is pretty rare getting banned in SSBB anyways. If I remember correctly, since 2014 we banned exactly two people in SSBB. I'd say more than 99,9 % of all bans are for Mario Kart Wii.