Shaking

Its not the cruse control. Check rotors (if warped), brake parts sticking, worn, Calipers with plastic and rubber parts and bolts bad. Tires/wheels need Balanced or bad tire or lug nuts loose, worn suspension/steering parts like ball joints, bushings, sway bar link pins/rods, tie rods, loose nuts and bolts ect. Your cruse control runs to the throttle body/intake and keeps the truck at a certain speed by use of the computer. I'd check tires first, or rotors/disc if you start to feel it when braking lightly. then if balance correctly and so on to the rest.

As enginecreator suggested, check brakes and front suspension first. Is the shaking speed sensitive?

Alignment issue or worped rotors, depending on severiness, it will be speed sensitive and that's why u notice when in cruise control mode