With regards to the design, I'm kind of meh. It's not bad, but not very exciting either. Seen much better.
With regards to the concept of mixing styles, why not? A similar post was made in the past and I noted I'd seen images on IG in the past that have mixed Japanese backgrounds with another culture's myths. Someone else posted a sleeve a bit back that had traditional motifs with a Japanese cloud background. It was cool to me. So saying that I don't see a big issue with the idea that an artist can make it work proper. Will it be traditional? Maybe not. Do you want it to be? Maybe. Maybe not. The key thing is finding an artist that can make it work though. Valerie Vargas seemed to make it work on I think it was an Athena sleeve and same goes with Chris Brand's Suikoden pieces. That's essentially Japanese (and Chinese) meets East LA culture and he's rocking it. Those people had skill to make it work. Many do not so hopefully you have found someone who can.
The artist seemed to go a different route than you originally wanted though. If you're not a fan, skip the idea and the middle man. I agree with others that you should work with a tattoo artist. And perhaps run with your original thoughts if that was what you wanted.
See that's the thing - I originally asked for an Oni mask and to include daffodils as a symbol of my nation - which is not too bizarre as it represents respect in Japan. The guy said he would rather do a skull of some sort and it went from there.... it was probably a mistake on my behalf for not just going to the artist I wanted the tattoo done by. The reason it was free because there was a delay in the design getting to me!
I'm not sure I'd want to mix in Celtic with Japanese. It just doesn't make a ton of sense.
Graeme is right though. Best to go to an artist who does solid Japanese work and have them design something for you, perhaps based on what you are showing us here, but more appropriate for the style.