If I understand what you're saying, your argument might be expressed as follows:
- If induction is possible for a certain type of facts, there are causal relations which are knowable with respect to those facts.
- There is no causal relation with respect to any fact about noumena that is knowable.
- Therefore, induction is impossible for any fact about noumena.
If that's what you're saying, I imagine that Kant would fully agree. However, it seems that you're suggesting that an adequate theory of induction would somehow allow for knowledge about noumenal facts. It that case, it might be helpful to note that the second point of the argument only applies in virtue of the fact that we have to rely on our senses:
"But, after all, the possibility of such noumena is quite
incomprehensible, and beyond the sphere of phenomena, all is for us a
mere void; that is to say, we possess an understanding whose province
does problematically extend beyond this sphere, but we do not possess
an intuition, indeed, not even the conception of a possible intuition,
by means of which objects beyond the region of sensibility could be
given us, and in reference to which the understanding might be
employed assertorically." (Critique of Pure Reason, A255/B311,
Because of that, there's no way to empirically acquire facts about noumena, so for all practical purposes, such facts don't exist for us. Therefore, Kant's philosophy would only suffer in comparison if there was such a thing as legitimate theories of induction which could claim extrasensory access to facts.
However, assuming that no such theories exist, we have to be satisfied knowing that the rising of the sun will always remain for us a phenomenal fact. Since causal relations with respect to phenomenal facts are knowable, there seems to no real obstacle to our drawing inductive conclusions concerning such phenomena. And that's what science has always been about.