That is interesting, that you put it in the same place where Copts and Ethiopians put it. Is the tattoo black or dark green?
Personally, as a Copt, I frown upon cross tattoos. In Egypt, they choose a specific color (blue or green) and the place (right wrist or thenar) for symbolic purposes as well as ID purposes in an Islamic-ruled slightly oppressive country that won't allow Muslims to convert back to Christian or would let kidnappings for the purpose of forced conversions into Islam go unchecked sometimes.
In the diaspora, I'm quite vociferous against the use of Cross tattoos because the idea behind it has not been taken seriously, and many people get it with nice designs rather than be humble about it. (It's interesting that even our own Coptic Pope does not have a cross tattoo.)
Like HG Bishop Youssef, bishop of the Southern US Diocese of the Coptic Church said, we need to tattoo the cross on our hearts more than our wrists these days.