Grounding Wire for a Microwave

I just moved to a new apartment in Fukuoka and bought a new microwave that came with the earth yellow/green wire. The only place I could ground it is an outlet high on the wall on the other side of my apartment away from my kitchen.

My main question is how necessary is it to ground microwaves in Japan? I know I should do it if I can but the only location is not a practical place for it. Would I be OK to just plug it into a standard two prong outlet and then just leave the ground wire unused?

OK to just plug it into a standard two prong outlet and then just leave the ground wire unused?
That's what normally people do here in Japan. You should be fine.

Those 3 prong outlet high up on the wall normally reserved for air-conditioner , most probably 220V AC.

I always assumed there would be one outlet on the kitchen wall with a grounding slot, either for a refrigerator or a microwave (or both).