Well Wraith Form, it does have rules for
Fear
so that is a good start

Characters Can (by the rules) eventually become
Jaded but for CoC you could drop that option since the COC things are So freaking scarry and Mind Bending.
The effects of the Fright Table are:
Heart Attack, Phobia, Panicked, Shaken, Panicked (again, yes it appears twice as a result on the chart), The Mark of Fear (suffers a cosmetic alteration -such as white hair, eye twitch,...etc), and Adrenaline Surge ("fight response" takes over.)
I would say a good way to stay true to (my impression) of the CoC rules is to have the more truly Cthulhu-esque monsters cause a penaly to the Fright Reslut, or maybe better, "roll twice and take the worst result."
The characters in SW are basically "heroic types" rather than straight up "mundain." So they will genereally be at least a little more inclined to try to fight a big nasty, but as the Gm you can fix that by making the big nasty, Really Big and Really Nasty! The players get "bennies" but so do really nasty special crtitters. There is also a small chapter on tips to running various campaign types, including Horror.
Also I guess that the Weird Wars stuff is a bit more creepy and one they are working on called "The Nam" has been said to have some Chtulhu type stuff.
If you want to do creepy horror type stuff the adventure from 12 to Midnight called "Last Rites" referenced above may be a good place to start?
Oh and!!!!
Actually without having to buy anything you can test drive Sw for a creepy horror adventure by going to
the "downloads" section http://www.peginc.com/Downloads/index.htm
and downloading:the Test Drive rules; and maybe pick up the Ranged Weapons pages with notes.
Then scroll down a bit to 'Adventures" and get:
The Eye of Kilquato (pulp era, July 1939, jungle adventure. It's it bit like a Doc Savage kind of thing- more adventure than horror, but a great demo adventure, and one I find can be used for Any setting rahter than just limited to the default pulp setting it is writen for. My players want to do it as an 18th Century setting.)
and
Shades of Terror ("This story takes place in 1920's Massachusetts" and refered to by them as "a Dungeon-crawl a la Lovecraft" it takes place in a asylum closed in 1911.)