I don't want to rain on your parade
but I think a cam mechanism might prove more difficult to implement than other possible solutions. Carel's comments are cryptic but correct; you can get an estimate of the torque required by considering the distance through which your final force acts, the amount of rotation and the throw of the cam. If you use a 1" diameter cylinder offset by 0.06" to get the travel you need you can just consider the static situation at half travel and treat the cam as a simple lever. However, it is Carel's other comment that is most significant; your will have to get a little gearbox that can take a 200 lb side thrust on the output shaft and that might prove to be a challenge.
There is also another problem and that is control; a little gearmotor unit will coast a considerable distance when the power is turned off and because your cam works by half a rotation giving the travel then the next half the retract you have to stop the motor exactly on the peak of the cam. You can solve this by using a gearmotor with a built in brake but you cannot avoid needing to mount two limit switches and have a bit of logic in your control.
Air cylinders are much simpler; you can just drive them against a stop and leave the air on. I have never heard of an air cylinder overheating when it is stalled. One suggestion I have is that you should consider having a small bore (3/4"?) cylinder with a stroke of 2 or 3 inches pushing a wedge to operate your lever. A wedge with a rise of 0.120" over a travel of 2.4" gives a 20 : 1 advantage so your cylinder force is only 20 lb assuming no friction. You can keep the friction very low if your wedge runs between two fixed ball races and the lever has another ball race rolling on the slope of the wedge.