Can I solder wall cord directly to servo?
First choice: Attach compatible, polarized connectors to both pigtails.

Alternatively, you can solder it up but the result is certainly less convenient to use. I like heat-shrink tubing for insulating wire-to-wire solder joints, one over each solder joint and a third, slightly larger one over both. (My favorite way to screw this up is to forget to push all three shrink tubes over the wires before I solder the joints. :)