Is "non-life-threatening" punctuated correctly with two hyphens?

Solution 1:

The U.S. Government Printing Office Style Manual (PDF), in paragraph 6.32 (page 120 of the file, which displays a page number of 103), says “Use a hyphen or hyphens … to avoid ambiguity.”, and gives “non-tumor-bearing tissue” and “non-civil-service position” as examples of correct hyphen usage.  “non-life-threatening injuries” seems to be consistent with those examples.

Solution 2:

This is one case where it's onerous to look at dozens/hundreds of entries directly within Google Books, but it's relatively easy to see what most people do by looking at Google Ngrams...

The pros and cons are covered perfectly well by Edwin's comment against the question, but with such a strong preference for "non-life-threatening" as indicated above, it's pretty obvious which one you should go for.