I preferred the invisible phaser beam in the original, ungraffitied "Naked Time." My off-topic comment, however, is why didn't Scotty simply cut through the door itself at higher power -- considering the urgency of the situation? In "The Enemy Within" the shuttlecraft is not mentioned, as it had not been introduced yet; "Naked Time" did not mention the intra-ship beaming used in "Day of the Dove."
The right way to proceed is not to cut a man-sized hole in the door; this will take forever. The right way is to cut a tiny hole where the lock mechanism is, because this will take very little time, and then use that hole to open the door.