The local university farm uses over the counter rubbing alcohol to dampen the sheared hair.  They dump it into a regular plastic spray bottle and give a couple quick pumps right after clipping and combing away excess hair, it supposedly gives a little better transfer of the cold iron to the hide. 

FYI, their own policy is no freeze branding in temps above 60 degrees to help with better cold retention in the irons as well as lower hide temps to begin with.

If your question concerns using this alcohol in conjuction with the dry ice (combined in the styrofoam container) I would think it should be the better quality alcohol to cut down on the need for more dry ice due to the extra boiling that will occur with the lower quality alcohol. 

If you're using liquid nitrogen for cooling the irons, you wouldn't need any of the 99%.