Nah, don't bother charging and discharging a cap like that. Just PWM it after the cap. The LEDs will be fine. Get a power supply of the right voltage, add a nice big cap at the output to reduce ripple in the power supply, then use a decent MOSFET transistor driven by some sort of PWM controller. Either high side or low side will work, but one may be a little more straightforward to implement. Generally low-side is easier to implement when you have to control something that runs at a higher voltage than the control logic. An Arduino could a PWM signal, or you could build something out of discrete logic or analog components (e.g. ramp generator and comparator). Doesn't really make too much difference.

Nah, don't bother charging and discharging a cap like that. Just PWM it after the cap. The LEDs will be fine. Get a power supply of the right voltage, add a nice big cap at the output to reduce ripple in the power supply, then use a decent MOSFET transistor driven by some sort of PWM controller. Either high side or low side will work, but one may be a little more straightforward to implement. Generally low-side is easier to implement when you have to control something that runs at a higher voltage than the control logic. An Arduino could generate a PWM signal, or you could build something out of discrete logic or analog components (e.g. ramp generator and comparator). Doesn't really make too much difference.