I used to smoke fresh oysters many years ago in my first smoker; Little Chief.
All I ever did was brine the fresh and rinsed oysters in the same type of brine I used for salmon. Let oysters soak in brine in the fridge for 24 hours and then put on a rack and tray in the fridge to allow them to drain for a few hours. I would always put tin foil on the bottom rack as they will continue to drip as they are smoked.
You can put a few dashes of your favourite spices on once they are arranged on the racks and ready to go in the smoker... garlic powder, chilli flakes, cayenne ect.
Alder is a good choice of wood for any seafood. Smoke them heavily and ensure you bring the internal temperature to a safe level. Seafood is prone to spoiling quickly and easily do you need to practise the utmost safe food handling procedures. Quickly out of the cold fridge and into a hot smoker always using clean equipment and work space. Once smoked put them on a rack and straight into the fridge to cool quickly.
If you make a brine, put a little aside before you put the oysters in it. Once the oysters are smoked and cooled then put them in a glass container and drizzle a little of the fresh unused brine over them. Mason jars work fine storage. Put lids on and straight into fridge. Don’t make more than will be eaten in a few days unless you plan to pressure can them. I’ve done that and it works fine but is a big project.
I always use glass or stainless containers for brining and storing food product. Hard to get decent oysters here in Alberta so I haven’t done them in years however they always turned out beautifully. I preferred the smaller oysters for smoking.
Let us know how you make out.