Your rhetorical question now has an semi-objective answer when it comes to actual usage!

ChatGPT-4 says, "In many cases, "a small fraction" could imply anything from just above zero up to perhaps 10% or 20%, although these are not strict rules."

It goes on to say that clarification is important if you need precision.

So, yes, 1 in 9 men could be considered a small fraction. It is much too big of a fraction, however.