These particular lighting fixtures are using 20 W light bulbs in each light and 6 of them connected in parallel will only draw 1A of current. So, 15A circuit or 20A would make absolutely no difference. Since the lights don't have a switch (as far as I could tell, it's usually on the connecting cable) - you may want to use a combination power outlet that has a switch in place of one of the sockets. This will require cutting the plug off the connecting cable and wiring it directly to the switch. Actually, I'm not certain it comes with a connecting cable, so that may be a moot point. Something like this will do:
It is a type of DIY project that I would only advise if you're familiar with safety precautions in working with high voltage wiring. But, since you're planning on replacing the outlet anyhow, I figured you have to be aware of that anyhow.
<strong>Be sure to disconnect the circuit at the breaker panel before opening the outlet!</strong>