I used to surgical clip everything, but some old-timers told me they got better results just using a close head on the Osters. Switched over in '05 and it does work better for me, as well as saving a bunch of time and sharpening costs.
My process uses liquid nitrogen, and the characters are continuously cooled, so it gets to -320 deg F in about 10 seconds and stays there. As dry ice/alcohol does not run as cold, and can be marginal with respect to keeping irons cool enough long enough, shaving may be the ticket there. Although as I recall (?), Gardener NE recommends close clipping only (not surgical) when using dry ice. They usually have a freeze branding insert in the sale flyer they send out in American Angus.
I do over 5000 head/year as a contractor and am happy to pass along info, so feel free to call.
Dave
406-560-2289
dave@freezebrand.com
(my website it old - 2003; but too busy to update, email for more current photos)
ps. Applying individually unique 4-digit brands, we routinely average over 25 head/hour with a good chute.