Stopping down the aperture (using a larger f-number) will have a two-fold effect. The FOV of the lens is narrowed slightly by stopping down. For example, on your 14mm lens, going from f/4 to f/8 would narrow the physical aperture from 3.5 to 1.75mm which would in turn reduce the diameter of the FOV by 1.75mm in a lens with rectilinear projection (slight more if its a fisheye) Moreover, reducing the aperture size will sharpen the vignette, causing it to "blur over" less of the image.

Assuming you cannot stop down the lens, consider this: Object path vignettes have no partitive effect. In other words, if your filter holder is forward of the entrance pupil, then the vignette will not act like a field stop.

In wide angle lenses the entrance pupil is almost always behind the front element's front vertex. This is as opposed to some telephoto lenses where the entrance pupil can be in front of the front element. In such a lens the effect of vignette would be partitive (cause darkening of some or all of the scene)

What does this mean? The area experiencing vignette is the only part of the image effected and that means that you can make your images and crop the vignette out in post.