This is going to depend on several things.
First of all, do you have a lawful, licensed copy of the SDK? My understanding is that Nintendo only licensed the SDK to selected game companies. If what you have is an unauthorized copy, you do not have the legal right even to use it. If what you have is properly licensed, then you do.
Or is what you have an unofficial SDK created by someone other than Nintendo?
Secondly, what does the license agreement that comes with the SDK provide? Does it require developers to register with Nintendo? If it does, you will need to comply.
Nintendo cannot prevent others from writing programs designed to run on their hardware. But they can control who uses their development software, if they choose to.
You cannot reproduce in your game any of Nintendo's copyrighted software (or anyone else's) without permission. That applies even more strongly if you intend to sell the software.
But you can use any development software for which you have a valid license in whatever ways its license permits. I would expect this includes creating games. It would include selling games that you create that do not use any of Nintendo's code, unless there is a specific provision forbidding that in the license agreement.