Thanks, WW and Jackie. Since the Daughters of Charity originated in France, they used the French -ette spelling for their headdress. All of the hospital archive material spoke of "cornettes" so I didn't think twice about the spelling, much less look it up.

And, WW, your comment about wearing hats up north because of the weather provoked an amusing mental picture of the aforementioned cornette on a blustry, snowy winter day. Flying nuns, indeed!