I don’t know anything about Wigner d-matrices, but all that is required for NUTS to work is a continuous embedding, ie an extension of your PDF to the neighborhood of the sphere. For example, if S is the sphere, and f(x) is your original log pdf for x \in S, an extension is
\hat{f}(x) = f(x / \| x \|) + g(\| x \|)
where \lim_{z \to 0} g(z) = -\infty to keep it away from the origin, g(1) = 0, and ideally g would fall quickly when away from 1, and be convenient for importance resampling.
(Note however that this is a theoretical scheme, whether you get efficient sampling depends on the details).