I've got a bag of hops hanging in one my kegs right now that I've been working on for 4 weeks probably, and I'm on the cusp of floating this keg. I did the floss tied around a 1 gallon mesh bag dangled about 1/3 way down, and the other end is tied to the keg handle. So far, no issues with oxidation or leaks. When I first sealed the keg I had to give a couple little pulls on the floss to get a good seal but I was sealing at serving pressure (12psi).
I also have a new, untapped keg with another bag of hops dangling in it. I sealed it at 20psi and then let rest at room temp for a week before putting in the kegerator under serving pressure. Again, so far so good on this one. I didn't have to give any tugs on this one to get a good seal (probably the little extra psi did the trick).
Edit: On second thought, you're talking about oak - wood. I have oak cubes floating in my bulk aging wine that has been floating for 1.5 months so far. Eventually they'll become wine-logged and fall but so far so good. You could, if you wanted, just let them float around and when you want them out use a sanitized slotted spoon (or similar) to retrieve them. It's not as simple as the suspended bag with floss trick though.