Hi,
I've used S-W tung oil on sporting and re-enactor guns for decades. The difference in their outdoor versus indoor finishes is that the external stuff contains UV blockers. It is meant for decks and outdoor furniture that are exposed to weather and sunlight daily for hours on end. The indoor stuff will work just fine for you. Hunting guns I built while living in SE Alaska were exposed to weather conditions most of you will rarely take your guns into. Those conditions also included sea spray while traveling in small boats. The stocks of guns finished with S-W polymerized tung oil held up very well. My guns are used on rainy weekend living history events, snowy week long hunts, damp gun gases, etc. No problems. One of my tung-oil finished guns was used to take a mountain goat in alpine terrain during a rainy period. It looks as good today as when made except for some scratches and dents. The only disadvantage to polymerized tung oil is that the shelf life is limited before it starts to gel after much exposure to air. The answer to that is divide your can into small mustard-sized jars sealed with plastic wrap and then the screw lid. The unopened jars will last a long, long time. You want to just pay attention to those who have experience with "polymerized" tung oil, not those who used raw tung oil, or Formby's tung oil finish, or minwax tung oil finish, etc. Unless the oil specifically says "polymerized" the results will be very different.
dave