OK. Not exactly quite what you asked for, I guess. But still relevant.
There is a short paragraph in the regimental history about the medal. It was awarded on 11-Nov-1879 (old style calendar). I could not find the list of awardees, but at least one is mentioned personally - Wachtmeister Nikolaj Shevelev - who received one of the ten gold medals for bravery. I could not find any photos of Shevelev, but there is a drawing of him. Can't really distinguish the Danish medal though...
Since regiments comander Colonel MEdvedovskij is depicted with his Danebrog crosses, I assume the Shevelevs portrait also should include the Danish medal.
By the way, though it is true that the specimen from the Mint collection is without suspension, The Orders and Medals Society of Denmark (OMSD) has an image of it with the suspension ring, but without a ribbon attachment.