Yes there is the manual of arms with the M16 just as with the M14,
If you google manual of arms m16, you will find illustrations of the process.
Inspection arms is a bit "odd" but can be done sharply with practice.
Yes, it does feel a bit awkward, but the light weight of the M16 helps make it look just as "military" as with the older weapons.
Our main "manual of arms" for the old M16 (pre-birdcage" flash suppressor) was to jam the open ended flash suppressor into the band around a case of C rations, twist sharply and break it (the band, not the gun) so we could get to the chow. Of course, years later, they told us we were bending the barrels by doing that.
But, I always liked the C rats.
The only long arm that I am aware of that had no manual of arms was the M1 Carbine.
Bob