There's a game (I have no mouth and I must scream) which I would like to play with scummvm. At the same time, I don't want to lose my playing time statistics on gog galaxy. Is there any way to solve this problem?
(the game starts with DosBOX as default)

You might try using this guide by mike_cesara for adding external games as a starting point. Instead of a "random" number for GameID, use IHNMAIMS's actual number so that it counts time for that ID (you might have to move the pre-existing file elsewhere or remove it entirely, and you should be aware that Galaxy might replace your custom file some time).