Thank you for sharing your question about screws for your handle.
It's great that you've received fantastic advice from @Brad. I suggest bringing the handle with you to the store to make sure that the screw fits. Looking at the picture you posted, I recommend testing this set Taskmaster M4x 50mm Zinc Snap-Off Screw - 12 Pack. It is a snap-off screw system that will allow you to get close to the same length as your old screw.
Please keep us updated, we look forward to seeing your handle restored.