I think you are correct. I believe he said in “Spare” that he once wanted to get one of Botswana while he was on that infamous Las Vegas trip but his friends and security stopped him, recognizing he wasn’t in the right frame of mind for decision making.I’ve never heard of Harry getting a tattoo, and I’ve been taking notice of his affairs since he was nineteen. That doesn’t mean he hasn’t got one though and people have just kept quiet about it.