No mythos required is a feature of The Haunting for me as well. There is an ability to turn the mythos dial but it is available to taste.
Should more mythos be desired I think Dead Man Stomp is a very good option. After that I would recommend Tell Me Have You Seen the Yellow Sign.
I think it’s good that CoC has its genesis in Lovecraftian horror - meaning that mechanically it’s about slowly going mad more than it’s about having your arm gnawed off - but it can certainly do a decent job of non-Lovecraftian horror that’s still more psychological than bloody.
And (considering last Whartstock) it can do slasher-film too.
That’s in an old Supplement isn’t it?
Tell Me Have You Seen the Yellow Sign.
While I don’t know the other scenarios from Blood Brothers 2 (or indeed the original one), I gather they’re each of a different horror-film genre, and basically non-Lovecraftian.
It is in The Great Old Ones. A collection I was lucky to have a friend introduce me to some time ago.
https://www.yog-sothoth.com/wiki/index.php/The_Great_Old_Ones_(Supplement)
The latest episode of The Vintage RPG Podcast includes a discussion of the starter set, beginning about ten minutes in.