There's more to soundproofing than just insulation. "Blocking" noise with a non-hardening caulk to close off airborne sound paths. "Breaking" the sound path using resilient wood studs with metal clips. Last, isolating and eliminating “vibration” with special acoustical matting that seperates the wall structure from floor vibrations. You can get all these items in soundproofing kits for both interior and exterior residential walls. Besides blocking most noise transmission, one obvious benefit is better energy efficiency, with greater “r” values.
Shop injuries often can happen when something is difficult to remove and excess pressure is applied. When using heavy force, especially with tools like a screwdriver or a needle-nose pliers, think ahead to what will happen if the tool slips off. If it could hit a part of your body, search for an alternative removal method.