One of my dogs chewed the corner of a coffee table and I'd like to repair it. Image below. I had filed it smoother and stained it, and we've been living with it, but the chewing is no longer a behavior concern and it's one of those things that should really be fixed or replaced. We'd like to try to repair it, if it can be done well.

I was thinking of scarfing in some new wood and trying to find a matching router bit, but I've never done that before on furniture and I'm not sure I have the skills. I presume I'd have to re-route the entire perimeter to try to make it blend. Alternatively there are sandable/paintable 2-part wood replacement putties (usually used for wood rot) that could be laid in and shaped, but then I'd have to use an opaque finish on the perimeter.

I could also try to find someone local who does furniture repair. Any thoughts or suggestions?