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It'll work fine the way you use it, but conditioning I think will make it a bit better. Just rub your hands on it every time you pass by.
You don't need to shorten it, only if you want to make it...

It's pretty easy to replace the leather part - afik they sell those at a good price.
BTW have you been conditioning it after sanding - that darkens the leather. The key is to use very little...