I don't understand why it would vignette. Isn't the shutter completely out of the way when its clicked, especially if you are using 'bulb' and a modified cable release?
I'm not doubting you, I'm just trying to gain a better understanding. Pinhole is completely foreign to me, but I've got an interest in trying it out.
The problems with converting the Brownie Hawkeye are that there are multiple points along the way through which the light must pass, and that the lens is some distance behind the aperture in the shutter plate (the glass on the front of the camera is just a thin protective sheet; the lens is mounted in the film holding assembly). If you just pop out the lens and install a pinhole plate, the aperture (and to a lesser extent the sheet metal plate behind it) restricts the angle of the light entering the body to the extent that it will vignette. The same problem exists if you put the pinhole in place of the protective glass on the front of the camera body.
Now, if you put the pinhole plate on the front side of the shutter assembly, you can resolve the problem, but it's not as easy a conversion. Not saying it can't be done, but the idea of just popping out the lens and putting in a pinhole - which was the way I planned to do it, as it was both easy and entirely reversible - doesn't work very well. You do need to add a cable release and tripod socket as well, but these are both pretty straightforward.