Oranges will eliminate the odor from nearly anything. Slice a few of them, put them on a plate, then put them into the safe. They leave a nice, fresh scent, too!
Many of today's air purifiers put out ozone. This is what makes that fresh smell like after it rains. If you have one of those, or know someone who does, put the papers so that the ozone falls on them. You may need to put them in a box in front of the purifier so that they don't blow around. You can also point the purifier into the safe for awhile and it should remove the odor. I have done this to my wastebaskets when they get an odor stuck in them with great success. I'm not suggesting buying an air purifier just for the papers, but I will say it has helped our allergies tremendously.
I have had good success with removing musty smell from trunks by putting dishes of coffee grounds in them. Dishes of baking soda also work sometimes. It takes awhile. If it is the documents you are attempting to freshen up, perhaps just exposing them to fresh air and sunshine will do it. I have not had great success removing the musty smell from books, but you could try the coffee grounds with the papers sealed into a plastic bag. Another thought, which I haven't tried, is to use those little packs of gel crystals that come in things -- some vitamins, new electronic equipment, etc -- these remove moisture from the air, and so might do the trick. In any case, they would likely prevent mustiness from occurring.
Add your voice to the conversation. Click here to answer this question.