Can I solder wall cord directly to servo? I have a servo which requires 7.4v and a wall power cord which says the output is 7.4v but the connector does not fit that of the servo. Is it safe to snip off the end of the wall cord and solder the internal wires directly to the 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. :)