Get Any Weapon
This trick works for primary weapon only, at least that is what I have found. First, set your multiplayer weapon preferences up. Then, when you have the desired primary weapon chosen, go back and select single player. Choose your mission, but do not press the right and left arrows next to the primary weapon on the weapons confirm screen. While the mission loads, the bottom of the loading screen will say you have the default primary weapon, but when the mission loads, you will have the primary weapon you have chosen.