SH can probably only influence DF in extensive ways (though I wonder if he still might do certain things like the black fire against all people).

kcf also reported: "This lead to lots of discussion about swearing to the Shadow – basically, it’s a very bad idea and you forfeit some very basic protections when you do. Shaidar Haran has special power over those that swear to the Dark One, and the Forsaken in particular. I asked about Alviarin’s special mark, and he said Shaidar Haran has similar power over her. The implication is that there are lots of ramifications for swearing to the Dark One. Brandon mentioned that this makes Verin all the more remarkable."

And it was stated in another report:
"Brandon hinted at some severe limitations on Shaidar Haran to affect the physical world. He says that a lot of actions that people assume to be those of Shaidar Haran in the book in one particular scene were physically carried out by Elza. He further indicated that Shadar Haran would have been incapable of physically placing the collar himself."

It will be interesting to see, how SH's grow yet and if these limitations will eventually vanish.