Yeah, a picnic tap is fine.
That said, adding a third tap is FAR easier than you'd think. As long as you have a 3" diameter tower (and you most likely do), you can add a third tap below and between the first two pretty easily. You don't even need a hole saw. With some patience, you can manage with a Dremel!
Here's my old kegerator...
The two top taps were already there. I added the bottom one with a Dremel. Easy as pie, although getting your fingers or tools in there to fit the nut on the backside of the shank for the bottom tap is a bit of a PITA. But all told, it's an easy job.