Swinger here
Style will determine the longevity of your injury free archery career. Any static weight bearing efforts, will increase the chance of injury over the same efforts done with dynamic movement.
You are correct also. BOTH need muscles to draw the bow. Static or not it's HOW you draw the bow and WHERE you end up. What ever alignment that is NOT proper alignment is WAY more subject to injury.
Learn to draw correctly and get proper alignment and you will be much more accurate also. There's a ton if info on the Form Clock thread on the shooters forum.