You will need a MT1 dead center -- there are several sources including penturners products.com. Littlemachineshop.com is a good place for small machinist parts and gear.
You have the choice of using the deadcenter - live center into the brass tubes and use of calipers to set size or purchase of special bushings. Normal mandrel 7mm bushings do not extend into the tubes, and cannot be used without mandrels. John Goodwin does make special mandrels which extend into the tubes and fit the live/dead centers -- so go to penturnersproducts.com for those.
I suggest the bushings for 7mm because it is easy to distort the tubes to too much pressure on the cone shaped live/dead centers. Without the bushings, you need to be much more delicate with the tools and pressure on the blank.
I have had very good dealings with John and expect you will have a likewise experience.
I turn both ways - with and without mandrel, and am growing to prefer the without mandrel. I use regular mandrel style bushings in many cases, but check them carefully to assure the are well made with holes centered and the ends square. I have a series of Panache style pens I am doing that with now. The solid feel allows confidence to be a bit more adventuresome with those pens which have more material to play with.