Sanding it out will create flat spots that do not follow the other contours unless you remove a lot of wood.
If there was wood removed in the scratch that may be your only "easy" option.
Try pre-heating the area with an iron and a little paper, no water. When it gets too hot to touch wet it with boiling water. I usually make a dam all the way around it with plastic modeling clay and get the wood very hot with the boiling water. Leave it wet for at least five minutes, maybe 10. Dry it with a heat gun or blow drier and set aside for a day to dry down deep.
I am betting the wood will have swollen enough to fill the scratch. Sand it very lightly with a block and do not try to get everything perfect on the dry stock. Finish the scratched area first with oil (assuming you are going to go back with oil) and apply heavily, let sit for 10 minutes and wipe dry. Let it cure for at least a few hours and repeat at least four or five times.
Then wet sand with water using a block. Now is the time to make everything perfect before finishing the rest of the stock. Fill any holidays in the wood or finish with superglue. The glue requires a great deal of care because it is much harder than the wood, sanding it causes issues. A fine file is needed to level the superglue.
Amine catalyst for the superglue makes the curing time instantaneous.
The superglue will likely disappear in an oil finish.
