SA is a breeze for rifles.........pull up SAP 520 on your computer and fill it out and send it to your hunter, and keep a copy on you. That's really all you need to do for SA, however check out your air carriers carefully as they have some pretty funky rules and virtually all of them want 2 weeks notice now if you are travelling with firearms. That and take a pocket full of Benjamin Franklin permits.........although you won't likely need them for exclusively SA. Elsewhere on the continent they are an absolute must, when travelling with firearms. Your hunter can answer all your questions and his/her info will be right up to date........best way for sure, instead of relying on internet babble. Rules can change almost daily but this has been my experience. Also make absolutely sure that you arrive at check ins at least 4 hours early when travelling with rifles and if the gate isn't open seek out a representative and inform them you are travelling with a firearm. It can be somewhat of a trying experience but as long as you are patient it is worth it in the long run. Always be polite and don't be impatient or rude no matter what transpires, as cool heads always prevail. I have had some pretty rough goes at airports but I just resign myself to the fact it is their country and their rules that I must abide by and answer all questions and produce all the paper work they request. If you have had the rifle since our old registry days and still have a copy, it is a very good idea to bring it, as many countries and their citizens have no concept of a country where firearms are NOT registered and will call you a liar to your face when you tell them that rifles and shotguns in Canada don't have to be registered. This happened to me in London, that's how ignorant a lot of people world wide are and I'm not talking necessarily 3rd world either. If possible avoid England at all costs and route through Germany or the Netherlands, Germany is very firearms tolerant and helpful, I have never gotten a hard time in Frankfurt. I have only been through Amsterdam once and as I recall it was painless.
The airlines are the biggest hurtle you will face, just make sure you contact them well in advance and make sure they will in fact carry firearms......some won't......and exactly what their policies are. Do this through e-mail and make sure you get the representatives name and everything laid out in writing as to their firearm policy. Print these out and carry them with you and do not rely on verbal statements. Or again you may be called a liar and set up on the "merry-go-round" for a couple hours. Make no mistake there are some very anti gun/anti hunting people working for the airlines and will go out of their way to make you miss a flight or inconvenience you in any way they can. If you run into one of these, and they usually are very obvious about it, ask for a supervisor immediately and make note of their name and lodge a formal complaint against them. This generally expedites things greatly, however if the supervisor is of the same ilk, ask for his/her boss immediately and don't take no for an answer, or threaten to call the Police which are usually not too far away. But you MUST know the rules and that airlines firearms policies inside out and have them in writing in your carry on, ready to produce instantly and prove your position.
Good luck and have a great hunt.......travel with firearms is not usually too bad, but it can be.