The spear gun isn't really a silent weapon, it might not have a noisy sound effect but then sound doesn't play a part in FOT. It's mostly down to line of sight, the only time sound plays a factor is when you are aware of someone on the opposite side of a wall, or they are aware of you. I say plays a factor but really the actors hearing each other is the only possible explanation for still being able to see their graphic (albeit greyed out) through a brick wall.
Firing any gun will automatically 'discover' you if you are sneaking. Other than the silent death perk used with h2h weapons. The only attack you can make while sneaking without giving yourself away is with grenades or molotov's and then IIRC that will only work if you target the ground near your opponent rather than throwing them directly at your opponent.