If we're going with some Marvel history here, Pinocchio was the inspiration for Ultron.
See, when Ant-Man created Ultron, he was thinking about wooden puppets. Upon discovering his family genealogy, he found out that he was actually a descendant of Geppetto. He travelled to Italy, and found the remains of both Geppetto and Pinocchio, and created Ultron.
But then, he was visited by the fairy god mother after she heard Hank crying about wanting a real sentient robot. She wished him Ultron's sentience, and that's how Ultron came to be. You'll actually notice in the comics that Ultron always has a sort of voice of conscience, but he'd always kill it, like Pinocchio and Jiminy Cricket.
So, it's appropriate that the song was playing because that's what Ultron plays in the comics to introduce himself. And his famous line is always "There are no strings on me."
This makes a lot of sense, right?