There are alternatives to stabilizing and if you are concerned about tipping the scales, do something along this line: wrap the segmented blank with a couple of layers of gauze and CA it. Put it on the lathe and turn one half of it down until round. If it is a delicate blank, wrap the just turned with a couple of rounds of gauze and CA it. Then turn the other half down to equal to the first half. This keeps it intact. If you think the blank is very delicate, do this gauze and CA a couple of times on both ends.
I have made a couple like this and my blowout prevention work might have been overkill, but at least I didn't have to look back and say, "I wish I had done . . ."