You shouldn’t have any issue with air in the cavity. If you vacuum seal them the vacuum will remove any air regardless of where it is. It’s not as if the cavity is anything like airtight. I have frequently vacuum packed whole chickens with no issues at all.
Edited to add:
I would treat them as I would any food that you were trying to freeze quickly which would mean spreading them out in the freezer. Depending on how much room you have in the freezer, you might want to consider keeping a couple in the fridge and freezing a couple and then when those are frozen putting the ones from the fridge in there.
