"You can project any image onto any geometry with any lens as long as they match" -- that's a big "as long as"
If you've matched the relative position and angle of a camera then there is only one focal length that will allow a photographed object and its match-modelled wireframe to line up.
Lining up the wireframe to the photograph is the bulk of the job. If you've done that, then you have already made a decision about focal length, camera position, and camera orientation.
According to a common misconception, image distortion results from the kind of lens one uses. In many people's minds, a wide-angle lens produces great distortion, while a telephoto lens "flattens images."
In fact the distortion arises from the distance between camera and object, and it becomes most apparent when a distantly-photographed object is unnaturally magnified by a telephoto lens, or when a closely-photographed object is unnaturally reduced by a wide-angle lens.
Close objects display distortion by virtue of their closeness. People associate distortion with wide-angle lenses because such lenses are commonly used to pleasingly frame close objects. The wide angle lens is not the cause of the distortion.
Distant objects display flatness by virtue of their distance. People associate flatness with telephoto lenses because such lenses are commonly used to pleasingly frame distant objects. The telephoto lens is not the cause of the flatness.
You can't DISTORT a cube without getting VERY CLOSE to it. No matter what focal length lens you use.
You can't FLATTEN a cube without getting VERY FAR from it, No matter what focal length lens you use.