I understand your hesitancy to take it apart. If you do, be certain to clean out the screw slots thoroughly, even a little-used gun will accumulate dirt and grease in the screw slots affecting even the best fitting screw drivers grip. On most box locks Ive had I will remove the stock and soak the still-assembled action in solvent overnight (I often use Coleman Lantern fuel). After a thorough soaking to soften any old grease, I blast out the inside of the action with carburetor spray-solvent using the long red tube to blast solvent deep into the action. The solvent is quit volatile and will typically dry if left overnight. After cleaning I relubricate the action with a light gun oil spray-lube, equipped with a long red tube to get back deep into the action. After lubrication I set the lock end-down on the bench to let the excess lubricant drain out. Ill also use a rag and Q-tips to remove excess lubricant that may have puddled in the mechanism. You can use compressed air to speed up much of the process. Lastly, I put the stock back on and its good to go. If not I take it to a gunsmith for lock repair.
Steve