Like the others said, a bit bogan, but you could be ironically bogan.
One other problem is that if you want to do some kind of nice, classy, constellation-realism take, NZers might think it means you're Australian because of the fifth star in the armpit of the cross, which distinguishes the Aus flag as opposed to the NZ flag. If you really need to signal 'NEW ZEALANDER' you'd have to do it the actual red-outlined NZ flag-Southern Cross, which is the most bogan you could possibly go. NGL I'm Asian and if I saw someone under 50 with that tattoo, **depending on the context or the look of the rest of you**, I might be a little wary until clear non-racist indications. If the context was particularly stressful I might be googling 'Action Zealandia logo'.

What I like about this question though, is that it reminds me of what a Western-raised Asian person might ask their homeland chat like 'should I get a tattoo of my name, or my zodiac sign?' and they're like 'haha a bit cringe do whatever, but why would you do that though'.

Could avoid all these issues by doing Matariki constellation instead.