There are a number of options here:
1. As Roy suggests, you can make a sleeve using a spare 7mm tube and either hardwood or corian. Drill and glue in the tube, and then turn it down to diameter that is a very slightly smaller than the ID of the 10mm tube.
2. You can buy a 10mm shaft to work the with the cutter that came with your 7mm mill. CSUSA sells shafts in various diameters.
3. Depending on the tube you are working with, you may be able to get away with using the shaft you have. That's probably not an option with 10mm tubes, but if you are working with 8mm tubes, using a 7mm shaft may be close enough.
4. You can look into some of the other means of squaring blanks. The most popular is a belt/disc sander.
5. I made a couple of tube sanders that can also be used to square blanks. These are simply small turned handles with a short shaft embedded in one end. I used bolts to make the shafts, sanding them down to match the ID of the tubes that they were intended to work with. Then, I glued a small bit of emery cloth on the end of the handle such that I can insert the shaft into the tube, and twist to sand the end. The intended purpose is to sand completed pen barrels to smooth off the ragged ends left when applying a CA finish, but there's no reason that this could not also be used to square the blank before turning (although squaring the blank using a small bit of abrasive would be much more work than using either a belt/disc sander or a pen mill).
One other comment - I recently bought some 3/8" kits, and because I knew that I was almost certain to screw up something, I bought a length of 3/8" brass tube at the local hardware store. Unfortunately, I found that the tube from the hardware store has slightly thicker walls than the tubes that came with the kits - and the ID of the hardware store tube is slightly less than the ID of the kit tubes. My point is that you may find inconsistency in the ID of tubes with apparently the same OD - so you need to plan on encountering the occasional surprise and having to find a creative solution.