For what you are using it for (removing CA from the end of blanks after turning), a sleeve is the last thing I want. I take a small piece ( about 3/4 inch square ) of self adhesive sandpaper, punch a standard hole in it, and stick it to the back of my barrel trimming head (the flat part) then turn the head over on the 7mm shaft. Hold the inside of the tube (any size larger than 7mm works perfectly) against the 7mm shaft (this holds it nice and straight) and lightly make contact with the sandpaper and slowly rotate the blank while making sure the brass tube stays pressed against the shaft. By not using the sleeve, you use a bit more of the sanding area and don't get a "ring" on the paper, it uses more of the sandpaper and gets a better, flatter result.
Now the sanding Jig you are using would do this just fine also, but I'm not crazy about the tension or potential for the blank to get grabbed by the disc and have some damage done to it. Granted I've never had one and never used one, but it LOOKS to me like it MIGHT have that problem. I may be wrong, but I also think if I can do something well, without having to buy something new ( I know, what am I saying...) that is a good thing...
Also, +1 on what Dan says. I've done that for barrel trimming, but I would add that I use the next smallest size tube that I have a shaft for, so most of mine are done with the Wall St II or smaller Baron tube, as the larger shafts are less likely to bend or flex.