Another thought occurred to me...
If the diameter of the wood is known, (for example, if you plan to turn pen bodies that are 3/8 inch in diameter), you could take a larger diameter length of round metal stock, maybe one inch long, and drill it longitudinally for the outer diameter of your wood. Then place this in a vise, and use a hacksaw to make a slot lengthwise in the part. Clean up any burrs inside with a jeweler's file. Now you can slide your wood into the adapter part you just made, and chuck this into the existing 3-jaw chuck. Just make sure that the slot is between the jaws, and not under one of the jaws. Tightening the chuck will tighten the adapter and grip the wood.
I have a few of these adapters that I have made over the years to save me time when I don't want to be bothered changing to my collet chuck to make one or two small-diameter parts. They work pretty well, and I have held material down to 1/8 inch in them, though you can hold smaller material, as well.
I don't know how precise you need to be, so I will add this caveat. I usually use a 4-jaw chuck, so I can indicate the material after installation and position it so it is as precisely centered as I need for my application. This may not be an issue for you, especially if you are turning wood, and an error of a few thousandths may be irrelevant.