Well he's already the least used player on the team so it's not like you can cut his ice time much, so the options are wait it out on the assumption his next injury is right around the corner or healthy scratch him and play Pezzetta.
The best long term way forward is convince him to go on permanent LTIR and that likely only happens if he's a regular healthy scratch. So in all honesty I think we shouldn't even wait the 10 games. They can ease into it by starting with back to back games, the first of which is Oct 23rd and 24th and then there's 3 sets of B2B games in Nov.
Does it even have to be a mystery illness, it's almost guaranteed that Gallagher is in pain every game, so like Price and Weber it's just a case of him deciding he can't/won't continue to play through the everyday pain.