While I don't know of any photographs of tattooed coat of arms of royalty, I do know of a heavily tattooed king. And although he didn't reign in the 19th century, being born in 1899, he is specifically mentioned in your link.

King Frederik IX of Denmark had several tattoos covering his arms and chest of styles very common amongst sailors of his time (Anchors, dragons, birds, the naval emblem of his country (A crowned anchor), etc.) which he had acquired the same as any other member of the Danish navy during his naval career (Before becoming king he had a career in the navy, and achieved the rank of rear admiral), and pictures of his tattoos as well as explanations of their significance are available at the Amalienborg museum.

Here's a picture that appears when you google for his tattoos

He did not, however, have a tattoo of his coat of arms. Probably because his coat of arm was quite elaborate. He might've gone for the Danish coat of arms (The three lions and hearts you see in his coat of arms), or his own personal seal (Basically a cursive R wearing a crown with IX printed below it). But going for the first one would leave out all the other parts of the Kingdom, so I imagine that would be problematic for a host of reasons.