The known proofs of conservativity of ZF + GC (Global Choice) over ZFC make significant use of replacement, and as far as I know the problem of conservativity of Z + GC over ZC is wide open. 

Let me add that I have discussed the problem with a number of experts over the past two decades, and also posed it on FOM in 2006 in [this posting][1].


  [1]: https://cs.nyu.edu/pipermail/fom/2006-February/010080.html