You can find out what C-c C-v does by pressing F1 k C-c C-v in a html-mode buffer:
C-c C-v runs the command browse-url-of-buffer (found in
html-mode-map), which is an interactive autoloaded compiled Lisp
function in ‘browse-url.el’.
That command can be bound in the appropriate web-mode keymap, aptly named web-mode-map: