I'm sorry to say that we don't sell anything in that precise size. Overall length doesn't really matter, to tell the truth, but hole spacing is essential and I can't find anything at 4".
Can you verify that? That's a very uncommon size. Make sure that you're only measuring between the center of each hole, not their edges.
It's very difficult to gauge this kind of size from a photo of a tape measure, however looking at your photo the center to center spacing does look under 4".
The final decision will have to be yours. What I can tell you with confidence is that there is no handle set in this style that I'm aware of that has a 4" hole center spacing, however 3-15/16" is fairly common. The hardware I've recommended remains our top suggestion.
Anytime, best of luck with the rest of the project and please don't hesitate to reach out if you had any questions.