I am familiar with the type of ball valve that you have; it is the Brewer's Edge valve. I have four of them myself. One of the posts mentions that you need a bulkhead. However, with this type of valve, anothe bulkhead is not needed.
Also this valve will work both the Igloo coolers and the Rubbermaid collers. You will need to remove the valve that came with the cooler and put this valve in its place. Insert the valve through the hole that held the first spout. Then from the inside add the nut and tighten the assembly. The o-ring in the valve should provide a seal so it will not leak.
You may have to have the handle at an angle rather than having the valve handle at a level position. This is so that you would have enough room to completely close the valve without the cooler getting in the way of the valve handle.
Finally, if you got the screen that goes specifically with that valve, the screen will attach to the inner threads of the ball valve. You may have noticed that there are threads on the outside and inside of the nipple.
If the screen nipple is the same size as the ball valve nipple, you might use a short union to join the two together.
I hope that this helps you.
Mark