Not sure what you are looking for exactly, but these are pretty cool.

Comments Help · More Info

I am looking to hang it over an outdoor dining table on the patio, under an overhang. There is an electrical outlet already. A plug-in seemed like a non-intrusive idea.

HomeGoods has a load of hanging lamps on chains and plugs. This is hanging Capiz shell lamp I found there and I just cut off the plug. I was going to hang it in my outdoor room but I tried it in my living room and loved it there.

You could use something like this. You would have to customize it with your own shade. Pendant Light

It says it is for back patio use.