Hitchcock's famous for his sharp-edged weapons. Probably the best-known, most iconic, Hithcockiest Hitchcock moment is the shower scene in Psycho, where the music goes screech! screech! screech! and then the murderer stabs Janet Leigh in the shower. (If you've got a strong stomach, you can watch it here.)
Psycho was released in 1960, fifteen years after Spellbound. But there's a foreshadowing of that famous shower scene when Ballantyne has a kind of psychotic break and starts wandering ominously around Brulov's house with a straight razor.
In Psycho, the knife is a penis substitute. The killer, Norman Bates, dresses up in his mother's clothes to murder young women. In fact, he thinks he is his mother, just as Ballantyne thinks he's Edwardes.
Bates is feminized—and Edwardes is feminized, too. He keeps fainting, when he should be heroing. He's weak; Constance has to take care of him. When Bates loses his manliness, he picks up a knife as a substitute, manly, penis-thing. And Ballantyne does the same.
The razor, then, is a sign of Ballantyne's castration (Freud was big into castration symbols, y'all). Ballantyne has lost his manly oomph, so he needs a razor instead.
You see this again with those giant, ominous scissors in the dream. All these sharp, cutting tools are a way of saying, "Hey! We over here are anxious about Ballantyne's lack of manliness, and are thinking about how his bits have been (symbolically) cut off."
The analysts could have told you this directly—but Freudian analysts in Spellbound don't like to talk about sex. (See the "Doors Opening" page in this section.) Hitchcock knew, though. He was already sharpening those knives for Psycho.