I've never hunted gators over at LANWR but I've hunted deer and nilgai there several times. If you need info on where the best places to stay, eat, ect. Let me know.
You might want to contact the area and make sure that a person that hasn't been drawn will be allowed to help. If they do, and...
Congrats! I've been fortunate enough to have done several of these hunts on the state lands but not the one at LANWR. It's not actually very difficult but hopefully you have someone to physically help you.
Go on Amazon and buy this...
IMO, if you have limited experience with a handgun, it will likely be very hard to shoot well under pressure regardless of the handgun. I think that a folding type pistol caliber carbine might suit your needs and be a lot easier to shoot under pressure. I personally have a S&W M&P FPC in 9mm...
These Mag-Spark 209 primer adapters work awesome. They will slow your reload time and they are not legal to hunt with in all states though.
https://www.warrencustomoutdoor.com/mag-spark.html