No doubt complete sanding and refinishing will be the best results.
However I have "prettied" up more tha a few with just 0000 steel wool and Tru Oil.
Buff the affected area with the steel wool, clean it up with alcohol, nad apply a few coats of Tru Oil, which can be buffed down and blended in with the steel wool to.
Almost always these will be visible under really good light but under normal light and conditions will look nearly as good as new, and it's a lot easier and quicker.
Nice thing is if you aren't happy with it, you can always go back to the complete sand down.