Dull Blades sabotages the Blighters' weapon supply so their blades do less harm. It is a cheap step in the sabotage line.
Dull Blades is entry 15 of 17 in the Ringleader branch, one of the three branches (Ringleader, Insider and Swindler) on the Rooks' 39-upgrade board. It is bought with money and materials, not skill points: £3,500, 50 Leather, 25 Silk. Before Dull Blades unlocks you need Poison the Well.