I have done extensive research on this. All the yogurt icings you see on dog treats, (where it dries like human cookie royal icing does) contains some form of sugar. They are just not always listing it outright or use other forms like maltodextrin or dextrose (which is just as bad as white sugar). They often will also use the terms, "yogurt icing, yogurt coating, yogurt frosting". None of which are just yogurt and most of which contain sugar or a form of sugar as the number 1 ingredient. If they have simply "yogurt" listed as the icing and it looks like typical sugar cookie icing - they are lying. I saw it a lot on Etsy.
Unfortunately, I don't think there is a way to get the look, design esthetics and preservation of royal icing for dog treats without using some form of sugar.
Thank you so much for your input, this will make me ask a lot more questions than I have before. It's so hard to know what is being put into what your dog eats. Now I know why I'm having such a hard time finding recipes.