I would just put oil on walnut. I use a mixture of equal parts boiled linseed oil, tung oil, and danish oil with Japan dryer. It has worked well for me for years. If you put it on thin, it dries relatively quickly and builds up relatively fast. That said, there is nothing really fast about oil. It helps to put the stock in the sun after a coat. In full sun, a coat should dry in two hours. Walnut will require a lot of coats. Once you start to get a semi-gloss finish on the stock, you are done. You just need to rub out the finish with a white Scotchbrite pad