I tend to saw to approximate shape, do a little rasping to true things up then fit with chisels, gouges and scrapers only taking out the wood I have too. Do there is always high wood. I used to do more filing as rasping but find cutting tools work better.
Once past the sawing and a little rasp work its almost all cutting tools. A very shallow 1/2" gouge, I have a 3 and a 4 Henry Taylor, can be handy when fitting the curve especially on a "difficult" piece of wood, pushing straight in from the side of the stock to cut away the high spots. This can be helpful if the wood has a lot of curl especially walnut the is often very soft between the "curl" and does not scrap or cut well vertically.
And as we all say, all tools must be REALLY sharp.
Dan