In almost all countries the male suicide rate is much higher than the female rate. The only country where the female suicide rate is higher is China, but even then only slightly, it's about on par I would say.

I have read it claimed before that countries with high suicide rates tend to be "shame" cultures, but if that's the case then surely doesn't that mean that the concept of "shame" only applies to men? Or at least applies to men far more than it applies to women?

I think the reason for this is that most cultures around the world are predominantly gynocentric and judge men much more harshly for their failures than they judge women for their failures.