Coq: why would you want to? I'm not that much of an Edison Company fan. I have enough cords around my grow as it is with: power strips, aquarium air pumps, fans, timers with figure eight cords to the lights, etc.
Side lights are okay but unless you rotate them to illuminate the entire circumference of your plants I'm afraid you won't find them the solution to your problem. There's no problem with A/G's lights if you have the tall arm/light stand and the hood that holds three flat high intensity CFL's.
Your admission that you have four plants in your little Aerogarden generally means that you probably have too many in that confined space. Two are good, three are a push but four in an Aerogarden are usually going to fill up the reservoir with roots below and give you too much vegetation above. You'll have plenty of light on top but most of the time it won't get through the vegetation to the lower portions of your plants where you also need it.
What you might want to consider are aimed reflectors bouncing the light back up to the lower portions of your plants that are mostly shaded. I used to use mirrors but they're heavy and if you break one, like I did, it's a dangerous mess. You might consider mounting some 2 mm Mylar on a solid backing and you'll get the same effect and they're feather light. I know it sounds crazy but you might want to consider it because you can get buds all the way down to the planting deck.