According to Rebecca, it is currently impossible for a Stack Exchange site's community to customize its How to Ask page:
This page is currently static across the network - it isn't set up to be customized per site. That is a fairly significant change, so it would need to be a separate feature request.
As I explained on Skeptics' meta, the page was written for Stack Overflow. It is perhaps most obvious when is says that "A lot of what we do is as much an art as a science, so a conclusive answer isn’t always possible." While that's valid way to remind programmers to "keep an open mind," that's not a good approach for other sites like CrossValidated, Math.SE, and Skeptics.SE.
In more general terms, the audience and the subject are different, and so the advices might be different. That's why it would make sense for each site to write its own How to Ask page.