Equipping Trinkets for Scouting

I notice that after a room fight, the scouting animation plays when I click over to the map tab. I'm not sure when the scouting actually occurs though for trinket purposes. Let's say I have ancestral map equipped and I want to unequip it before a room battle to avoid the extra stress. After the fight ends can I then equip it before switching to the map tab, or has the scouting already been determined by then? This is also relevant with Houndmaster's scouting whistle since I won't want to snuff the torch after a room battle if it's not going to improve the scouting anyway