You are on the right track with Truoil. I use it exclusively. You may want to lightly clean the wood with fine bronze wool before hand and MASK OFF THE CHECKERING. Put it on by inverting the tru oil bottle using 2 or 3 fingers on the top, then using the oil you have on your fingers now to rub the oil into the stock. Rub it until it feels warm on your fingers. Let it dry 12 hrs or more then bronze wool the whole thing again and repeat the process until you get the finish you want. Satin finish? Wool it again and don't re oil. Browning/weatherby finish, keep wooling and rubbing then buff after the last wooling. You want to put the finish IN the wood not ON the wood like paint.
The best cold blue out there comes from Brownells. It's called Oxpho blue. Use the cream NOT the liquid. Be patient, use fine steel wool to burnish between coats, follow the instructions but let it dry over night. Do multiple coats. Not as permanent as rust blue or hot blue but for your purpose it's the best way to go. Here is a link to Brownells oxpho page (shipping is a killer )
4 oz. Oxpho-Blue™ Creme : OXPHO-BLUEŽ CREME | Brownells
Thanks Art.