I've actually gotten Tri Force Heroes to work with HANS on my 10.1U New3DS XL.
HANS is not needed to make Tri Force Heroes run in any way shape or form for a N3DS on 10.1
The game requires a minimum firmware of 9.9, so your system being on 10.1 passes that check, and also means your are either using a retail cart or an eshop download. Unless you are trying to say you managed to get a .3ds file to load on 10.1 with Sky3DS, in which case I am going to call you a liar until you show documentation proving it worked and detailing how you got it to work AND it is verified to work by at least 3 other people who own a Sky3DS.