Old hammer found in my grandfathers shed

In the group of tools that my mother found in my grandfathers shed was this hammer.  It appears to be a straight pein hammer.  It has had the crap beat out of it.  The flat face is a complete mushroom.  There are no markings on it other than a "3" stamped on one side of the head.  I'm guessing that is the weight. 

The handle does not have a wedge.  The head is simply friction fit to the handle.  I have not ever messed with this type of hammer so I have no idea if it should be wedged or not.  The eye is slightly larger at the top of the head than it is at the bottom that leads me to think it should be wedged.  The head is so beat up that the difference in eye size may be due to damage. Any ideas or direction on whether or not it needs a wedge would be appreciated.  

Below are some pictures of the hammer before and after.  I used a wire brush in an angle grinder to take off the rust.  I don't think I will grind off the mushrooming unless there is a compelling reason to do so. I will oil the handle with BLO and mineral spirits, but I want to decide if I need to wedge first.