Is this feasible? What parts do I need?

I don't understand your question. The SSR is just a solid state version of an SPST (single pole, single throw ) relay. You simply cut the LINE (HOT) wire of any 120vac powered device, no matter what it is and connect the two ends of the wire you just cut to the output screw terminals on the SSR (they're labeled). Then you apply a dc voltage from 3V to 24V to the INPUT screw terminals
(+V,GND) and either use a digitalWrite output to drive the INPUT of the relay or PWM , as already mentioned. Since I don't know what you were asking I don't know if that answers your question.