Update CF 7 v3.8 safely?

This hosting client of mine has an old version of CF7 (3.8) and there is no Integration option for the plugin. His forms are very important and wants reCAPTCHA v3 which, I assume, will work in the background IF I can update the plugin SAFELY?

(Version 3.8 | By Takayuki Miyoshi)

The page I need help with: [log in to see the link]