The military ramrods were probably wrought iron.
Steel wasn't commonly used for parts that didn't require its special properties until after the Bessemer furnace was developed in the 1850's.
Reading thru the Handbook for Riflemen, (thanks for the page reference) I notice a few interesting things:
The grooves impression on the outside of the rifle ball makes it spin like an arrow.
Backwoodsmen commonly used the cupped hand with a ball in it and then covered it with powder to measure their powder charge.
The ball should be sized to "rest on the grooves, and require not much trouble to force it down, but not yet to pass without being forced."
The patch "Is a small piece of shammey (sic), or buck skin, or kid skin put round the ball before forcing it into the barrel...care should be taken that it be not too thick and defeat its purpose...it is used to take off from the windage, to retain the air, and the grease is used to facilitate the passage of the ball by diminishing the friction."
Either hat or leather pieces were used as wads which were positioned over the powder charge and over the ball if one was intending to march with the gun loaded. Linen, cotton, woolen cloth or paper could also be used for these wads.
I didn't see any further instructions on how to load a rifle.
There was no reference was made about using a short starter or any similar item to start the patched ball.
This doesn't totally rule out the use of something by the riflemen but it does seem the manual doesn't give any advice about what could be used or how to use it.
It does tell us however that washing your feet every morning in cold water makes the use of socks unnecessary.