I would not carry a crop/whip/stick in G&S. I've never come across anything in the rulebooks for the shows I participate in that outlaws them in G&S, but touching the horse in the ring is going to dock you points no matter what you do it with. In terms of G&S, I would highly recommend working through whatever nippiness he has at home before taking him into a show situation. Even in halter, which does make use of a "show stick" in some cases, frowns on disciplining the horse in the ring. All of that should be under control at home, before the show.
As I said above, halter exhibitors sometimes make use of a show stick, whip, or cane, but it is not intended as a preventative or disciplinary tool in the ring. The stick is a positioning tool, in order to better position the horse, direct him, and therefore show him to his best advantage. Personally, I have only ever seen sticks or whips in halter classes used by entries in Saddle Seat turnout, or in draft halter classes. Western and Hunt Seat entries in a simple halter class (for example, Registered Quarter Horse Mare Halter) do not carry a stick.
Halter and G&S are not discipline specific - you can wear whatever discipline attire you want in either class. G&S is typically divided into English and Western divisions, and in 4-H the only difference between the two is that a turn on the forehand is acceptable in lieu of a turn on the haunches in English attire. Halter simply judges the conformation and gaits of the horse, non-discipline specific. That being said, a horse with more park-type action in Western turnout will probably be docked points, as he is not being shown to his best advantage.
Lastly, read up on the rulebook if your show is being run by a specific club or organization, and ask at signup if you're unsure about the legality of any of your turnout or equipment. It never hurts to ask.