A couple of things you may consider.
1. I did not have much success in holding smaller knurled knobs/round stock in a 3J, both from a being able to hold it and keeping it parallel when the piece was short (like 1/2" or shorter). A 4J usually has coarser jaws that mar up the knurl, 6J would be better in distributing the load if you have the $$$. I had problems with the pieces shifting when turning and not being able to hold the piece parallel to the chuck face in my 3J. I do not have this problem with a collet system, and I do a lot of small items where less than 1/4" is being held in the collet.
2. I use brown paper bag cut in strips to wrap around delicate pieces, usually one layer in a collet type holder, 2 or 3 layers at each jaw on a 3J or 4J. Do not use masking tape, the piece is guaranteed to twist and move with tape. Brown paper shopping bag material lightly compresses and has a high frictional capacity. I have no damage of knurls in different materials using the paper bag and a collet system, especially in softer materials, but it has also worked well with my 3J and 4J. I tried brass stock at one point, it did not work as well for me. Brown paper bag shim also works well in a collet system where you trying to hold a piece (like your knob) which is between collet sizes, I use the larger with a single layer of brown paper bag, works like a charm.
On the collet system, if I need two layers, I cut 2 strips, just slightly shorter than the diameter of the piece, wrap them around the part like an onion peel, then insert into the collet. If wrapped as one piece in a spiral, it may not clamp symmetrically.
3. Of note if you decide to do more turning of small short stock. Use a collet style chuck to hold the piece, only applies to stock 1" and smaller. This is what I routinely use, it works well with one caveat. When you knurl, you displace the material and the diameter gets larger. If using a 5C collet system, if you started out with something like 3/4" stock, it will now be about 0.02" larger in diameter after knurling, and will no longer fit the 3/4" 5C collet. You need a full set of 1/64 increment 5C $$, I found this out the hard way, as I accumulate more over time.
4. If you only do this occasionally, and on short stock, consider an ER-40 system, you can buy or make a Hex (for 3J) or Square (for 4J) ER-40 block holder for about $30. Chuck it in in your 3J or 4J and use an ER-40 collet which has a much wider clamping range.
5. Last but not least, if you want to end up with a knurled rod that is 3/4", you need to under size the rod slightly before knurling. Also, sometimes the knurling can be a bit rough on the hands or too pointed, I either take a light cutting pass to take off tops of the points, and or lightly sand the tips, and put a small bevel one either edge of the knob.