Got 5 dogs in one morning using #4 steel. Dusting predators with shotguns is more about pattern density. I don't recommend #4 steel but it will work. I'm a big fan of copper plated BB's, pattern density is good. #4 buck shot is superior to 00 in my opinion due to the pattern density issue.
On another note, I've become a big fan of Federal's flight control wad. I've used it primarily for turkey hunting using #5 or 6 lead shot and have flattened birds at surpisingly long distances. Due to the success I had with #4 steel (not Federal FC wad) on the wonderful morning previously mentioned, I picked up some Federal Prairie Storm BBB's that do have the FC wad. Less than $20 per box of 25, I hope to try them on yotes soon.