Id say it wouldn't be a problem for you to teach. Although check the Institutes that offer the services for you to teach abroad. From having a quick read from the JET program it could be a possibility you may not be able to apply through them since Greece isn't a participating country and also because of one or two other details.

Check around and find more information, have a look at TEFL either and see what information they can provide about being able to teach. There is a few other type of institutes that also offer services of being able to teach in Japan (not sure of the names though).

I'm sorry i can't provide much more details, iv skimmed through information regarding teaching as a passing interest but wouldn't know too much regarding it.