So we have:

 - Where-Nowhere
 - When-Nowhen
 - Who-Nobody
 - What-Nothing

Why can't we also have "nohow" and "nowhy"?

"No reason" works to some extent, but "nohow" isn't really replaceable in a concise manner, to my knowledge.

The real question here is not how to say it otherwise, but why it would be horribly wrong to use it. And would it?