It is easy, and works well, IF you know what to expect. Here's what we do, and what you may expect based on a repeat of my past experiences. There’s probably much more information here than you were asking for, but I figure more is better than less.
We fly PHX to CLT or ATL (airline depending) to SXM and on to SBH. We always check our luggage all the way through. Upon arriving at SXM, you exit the jet to the tarmac often through both the front and rear of the plane, enter the terminal, but you do not clear immigration; instead, you will pass a single lane security area on your right, along with "ticket booths" for three or four airlines, WinAir being one. It's not unusual for these to be poorly or non-staffed. Stand there for a while (will seem like an eternity, but remember, you are now on Island Time). If no one comes to your aid, try the security guards at the checkpoint to your right, ask if they could assist you with summoning a WinAir representative. Usually you will get a "WinAir will be right back", and they are, eventually, correct. Once you get WinAir service, proceed through the security check point, and as you walk forward to the apparent gate area ahead of you, look for the stairs on your left to the upper level, take them, and continue walking in the direction you are now traveling (being after you did the 180 turn around to head up the stairs) and walk (or run as the case may be depending on how much time you wasted waiting for the WinAir agent) to the far end of the terminal where WinAir is located. Check in with the agent, ask if there's room on any earlier flights if there's considerable time until your departure. Once it is time to board, expect to pass through the glass doors, descend about half way down the stairs, and sit or stand on the stairs until they open the door to the street level bus shuttle you to the WinAir flight. Try not to think about how you would be trapped if there was an emergency; panic attacks are a bad way to start your trip. Proceed to your plane, sit directly behind the pilot for best some good sights. If there's no copilot, ask if you can ride shotgun. I did so one year and he turned over the controls once airborne. Little did he know 30 seconds is my best time in Microsoft Flight Simulator. If you are unfamiliar with the SBH landing, research it so you are not surprised, or wear Depends, the choice is yours. You used a key phrase in your question… “not getting the bag”… and we’ve only had this experience once, and after three days of checking for luggage at the oh-so-small airport, the ticket attendant said “nope, not here today either, but what does it look like?” To which I responded “black with red rope on the handle”. He looked surprised and returned with the bag and explained it had been there three days and was wondering if someone would claim it and asked, “why didn’t I tell him”. Duh!!! Anyway, one doesn’t need many clothes in SBH so it really wasn’t a big issue after all. We always carry on long pants, shorts, swim suit and flip flops – the bare essentials to survive lost luggage.
Since I'm writing what has turned into the novel of my travels, I might as well give you the return details. We always leave SBH early, checking luggage all the way home. We arrive SXM, check in with our airline for boarding passes, and grab a cab to the Sunset Beach Bar (where topless women drink free) at the end of the runway. We hang out there until 1.5 hours before our flight. Just ask staff for a cab, they are always nearby. Each trip is about 10 bucks and they often don't seem to care if you pay Euro or US dollars, so pay to your exchange rate advantage, of course. CLT always seems to be an immigration nightmare for us, and we often miss our PHX connection. ATL, a possible connection for you since you’re flying Delta, seems to handle it better, but you have to reclaim your luggage and check it through, a very expedient process. We always keep the day after our return wide open to be able to handle any missed flights, plus heck, why am I in hurry get home anyway

. Hope this helps.