If the scratch isn't particularly deep, you can just sand the wood around the scratch down so that it reaches the same level as the bottom of the indentation. That way, the wood will be uniform.
For outdoor use, I recommend using Douglas fir or vertical grain Douglas fir. These woods hold up very well in outdoor conditions over time. For indoor signs, good choices are...
Use a furniture refinisher to dissolve the stain and scrub it away with a bit of steel wool. Although it still involves some scrubbing, this approach is less damaging to...
You probably want to lay off of the acetone and abrasive chemicals for a while. Just give your nails time to recover naturally, since you may be drying your nails...