The few times i was really worried about such quick escape; i tied a slip knot in the lanyard to the side D a few feet from the snap. Then, snapped my saw snap (light duty) into the lanyard snap. Whereby ditching the saw; would give quick release as it pulled release side of hitch to lanyard, and catch the saw in 1 action; no hand pull required. The light duty snap/strap would let go if it got whatever force on it (stuck in tree top, as it fell forces would break).
Couldn't totally recomend it; just how i dealt some extra confidence in safety in some tough spots. Never really tried it in actual emergency.