I have no trouble believing that Scotty would have spent a lot of time near the galley...The galley scene. I'll skip the phaser locker and ask why Uhura and Scotty show up to question why the alarm went off. Don't these guys have more pressing things to do? Is it just to bring our main characters back into a scene together?
Which, in turn, explains the cooks' phasers.
Actually, the funny thing is that Scotty seems to change pretty much everything: his undershirt goes from white to yellow when he swaps the vest for the jacket...All he has to do is take off his utility jacket and put on the officer's coat, he could have done it on the way to the transporter room.
Is probably just sweat stains that made it appear yellow.