Part #4104 was a dress up sleeve that slides over the exhaust pipe. It serves no purpose except to provide a little bling.
The muffler slides into #1506, which is an aluminum casting that bolts to the head, same as a Model M. Simplex changed from a slip-in to a slide-over on that pipe sometime in the later 1950's, as the earlier style always leaks a little oily residue. Muffler #1504, is the correct short style for your bike. The long dual exhaust was not available until after 1954, I believe.
There is no strap for the short muffler. There is a 1/4-20 bolt with a turned down tip that gets tapped into the aluminum manifold. This is drilled in place when you install the muffler. On the exhaust pipe there is a hole, which gets bolted to the front engine mount bolt.