Well first of all, it is good you recognize side raises add shoulder width because they do develop the lateral head of the deltoid. Unfortunately, to best develop that head you will need some variation of them at all times. Some variations include dumbbell, cable, behind the back, to the front, lying on the ground, or lying on a bench at a 45-degree angle.
Other popular exercises (which work other parts of the deltoid as well) include behind the head shoulder presses, which requires strong rotator cuffs and good shoulder mobility, but is amazingly effective.
The below mentioned cleans are a good option and can be performed with a barbell or dumbbell, from the floor or hanging.
Nevertheless do not forget the posterior deltoid either, which gives your shoulders a more 3D look and some argue even push the lateral deltoid even farther out. Face pulls or bent over lateral raises work it well along with cable pulls across the front of the body.
Good luck and train hard.