What was the smallest gun that could threaten Scharnhorst?

What was the smallest gun that could seriously threaten Scharnhorst?

Six-inch guns, based on their demonstrated effect at the Battle of North Cape, though range and hit location still mattered.

The six-inch gun is the practical lower bound shown by combat evidence. British six-inch weapons performed usefully against Scharnhorst during the Battle of North Cape. The result still depends on range, ammunition, angle, and the part of the ship struck. Those hits demonstrate a threat without proving that every six-inch shell could penetrate the main armor belt.