Steam doesn't actually have an option to stop updates happening. The most you can do is delay them until you next launch the game, unless you faff about with disconnecting your internet connection temporarily while launching the game. It used to have that option, but it was notorious for ignoring/resetting that setting and at some point Steam has simply removed that option entirely.
One option that may be worth exploring, that I know at least some games use, would be to make use of the beta tab to keep old versions available as opt ins. Steam will then not force an update unless that particular branch is updated.