It would be best for you to use a 25-30W iron with a flat tip. This will help for the section to heat up more and spread out too, as opposed to a point tip. Also use a little bit of solder flux on the area that you will be placing the ground wire tip (OR, dip the end of your ground wire just a tad bit into some flux). Clip the wire with an alligator clip, or hemostat, to add some weight to hold the wire in place so you won't have to futz with too many things at once. Use a pointer stick, chop stick, whichever, to keep the wire's end flush with the claw if you have too, then go to town... Just a few seconds, if that long, until you see the flux react with the solder, you'll notice the solder flow, release the iron tip from the spot and let it cool. EZ.
But yeah usually those connections take a bit more effort than a wire to a lug or spade.