The situation is less dire than I assumed. About 90% of the users do in fact use the latest Chromium WebView. This number is based on several hundred million hits in December 2015, primarily from North America and Europe.
The full results are here, split by device vendor. In general, well over 80% of the users of a particular vendor use the latest (Chromium 46 or 47) WebView. Although there are a few vendor with less modern WebViews (Asus 44%, Kyocera 60%, ZTE 64%), they are small fry compared to Samsung, who scores 88% on modern WebViews and is by far the largest vendor in this sample (69%). Anyway, take a look for yourself.
Thus, at least in North America and Europe, you can reasonably expect most of your users to have the latest WebView installed. In Asia, especially China, the situation may be different, since Chinese Android devices are decoupled from Google, and vendors may work on alternative WebViews or simply refuse to update the Google ones. Unfortunately this dataset does not allow us to draw conclusions about Asia.
Also, this snapshot only counts users who actually use apps to surf the web. Those that don’t may have different update patterns. Then again, we don’t have to worry about people who don’t surf the web.
Anyway, there you have it. Although the Android update process is still broken, most users tend to use the latest WebView. Many thanks to Scientia Mobile for sharing this data (and they may share more in the future).