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It’s better than what it was!
Perfection is not needed for every project, some things just need to work.

I think the box is leather covered and shoe dye would work. If you were really into leather they have a ton of water based pigments you can mix for colour. Most people would likely find the shoe...

I would get a nice hinge from Lee Valley to repair the lid. They have some nice an inexpensive hinges for small boxes

The box in the OP is a seven day box. The way the razors are arranged it looks natural but there are three spaces for razors not used.