Regarding the form, family registers are handled by local municipalities so you'd have to know which municipality to go to. For example, here's the web site for Shinjuku in Tokyo.
不受理申出:新宿区
I think the main purpose to doing this would be to protect your rights in Japan especially if there are minor children involved.
But since you are not living in Japan anyway I'm not sure what this would accomplish.
Assuming your marriage is on the family register, this might prevent her from divorcing you on paper but it wouldn't prevent her from moving back to Japan and abandoning you. But as Thomas said, I would try to contact the organizations listed on the Rikon Alert site to see what they think about your situation.
Best of luck to you.