In particular, what do you mean by CH without choice?
CH in that context then is just that there are no sets of cardinality between that of R and N. You can't phrase it in terms of alephs (since without choice alephs aren't necessarily well-defined). As for a citation, I think Caicedo's argument here can be adopted to prove the statement in question.
I said that I doubt your claim, so blog posts proving different things aren't very convincing. Maybe I'm confused by the difference between choice and well-ordering, but imprecise sources aren't going to clear that up.
In fact, it was Caicedo's post that lead me to doubt Buie. Everything Caicedo says is local. In particular, he says that CH(S) and CH(2^S) imply that S is well-orderable. Buie makes a stronger specific claim that CH implies R is well-orderable, which sounds like a stronger specific claim, unlikely to be proved by local methods. I guess it is ...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.