I still think a partnership with Microsoft would make more sense and be more beneficial to Nintendo/gaming fans than going third party if it comes to that.
It would ensure Nintendo could have control/say in hardware and as the primary lead company for the platform, they'd be under pressure to continue making a wide variety of content so as fans we could be assured similar software support from Nintendo.
But they'd also have their answer to a wider audience in the West/"dudebros" audience/third party issue and MS would be a very nice partner in complimentary content ... Halo, Forza, Gears of War, Killer Instinct, ReCore add badly needed Western diversity to Nintendo's offerings, while other Rare IP like Banjo-Kazooie could be revived successfully and then you could have tons of Minecraft tie-ins (Minecraft x Pokemon anyone?) which would be great for kids.
Third party IMO, they'd get under pressure from shareholders to simply make the same 5/6 most profitable franchises over and over again just like EA/Activision/Ubi Soft do. When there's no obligation to a platform, there's no reason to make a wide variety of software titles.
Also not being able to cultivate an audience by having control over it means franchises like Splatoon, Animal Crossing, etc. probably don't take off. On a Nintendo platform every Nintendo release is notable, and a new Nintendo IP is given a lot more attention than it would otherwise, this cultivates a general audience base that buys most big Nintendo games. You don't have that as a third party.