Just as the title says. Anywho, this is a question that has been on my mind for awhile. Is there any benefit to having a weapon in one hand, but nothing in the other? Do I block faster than with a shield, or is blocking speed unaffected? Also, do I still gain the benefits of all the blocking perks or only a few?

Having one hand used for nothing is same like playing a game on PC with one hand when both mouse and keyboard are required. It's possible, but not as efficient.
Blocking with shield is as fast as with one handed weapon, there is no difference in it (I am broad'n'sword player, didn't notice the difference). As for perks, you will get slow-mo time when you block, even if you use one handed/two handed weapon with no shield. Also you will be able to do powerbash, and disarm. As for other perks like elemental protector or shield runner, you need shield