I've been playing with public and private headers on my New 3DS (JPN) with the WiFi turned off. When I want to use WiFi to check eShop or whatever, I switch to a private header game on my Sky3DS or eject it. I've had my Sky3DS for over 3 months and haven't gotten banned this way. I'm making the transition to make all my games on my Sky private using my own headers. I think it's okay using the Sky 3DS as long as the WiFi switch is off.
Edit: Most of my games that use a private header use the exact same header from one game. I only have like one or two public header games on my Sky3DS.