Patching a narrow scratch on mahogany door jambs?

I pushed a chair through the doorway side jambs of mahogany wood. It left gouges through the corduroy material as if they were the finish nail heads themselves. They are right through to "white" (unstained) wood. But they are not gouges that require an undercutting. Sanding along the surface would do nothing to help. Generally only 1/16" wide, by less deep. Deep enough. If you say I need mahogany stain colour sawdust, then I have some. What to do
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