What's the dremmel for ? Are you trying to turn it into a pick & place machine or a router or maybe both ? Dremmels are actually quite heavy or would be for such a machine & the motors being small might not be up to the cutting forces of a router.
If it's just as a pick & place machine picking up small items then if you can't find small enough linear bearings a bit of thin diameter stainless rod & iolite or phosphor bronze bushes might work.
If you want to fit a cutting motor then maybe best to make one rather than use a dremmel, Tenson made one for his machine that he advertised for same which looked to be quite light & using a smaller motor you could probably make it even lighter still.
http://www.mycncuk.com/forums/items-...t-spindle.html