eep, this is a toughie. I've lived in a place that had mice while having my budgies, but I also had cats at the time and the cats made the mice leave. They were very attracted to the budgies' food.
If you can, store the food in another room than the budgies' cage. Make sure to clean the budgies' cage and all around the cage after every meal. If possible, move the cage to a different room completely as well for a while.
Snap traps are also very dangerous to your budgies, so I would not let them out in a room where they could encounter a trap.
Cinnamon is fine for budgies to eat.