U.S. Navy photo courtesy of Northrop Grumman by Alan Radecki
National Naval Aviation Museum via Rick Morgan
And then there was at least one Regulus missile launch using a cart:
Since the Brits were first with just about everything concerning carrier-based operations, I wouldn't be surprised if they had held the honour on this achievement as well.
But congratulations to Northrop Grumman and the Navy nevertheless. The launch itself is actually not a big deal; F-18 pilots aren't even supposed to have their hand on the control stick during the launch. The taxi forward and hookup to the catapult unmanned? That is a much bigger deal and the X-47B is the first to do that.
The arrested landing on a carrier of an unmanned airplane would also be a first for sure. But not the first hands-off arrested landing. That was done more than 50 years ago. See http://thanlont.blogspot.com/2011/07/look-no-hands.html