what is a monkey man in the navy?

Answer 1

MONKEY An adjective formerly used afloat to describe any small place or article, e.g., monkey jacket (i.e. abbreviated frock coat), monkey island, monkey boom, etc.
"Black Dog for a White Monkey"
To "give a black dog for a white monkey" is an old naval way of expressing a fair exchange - a quid pro quo.

Answer 2

Not sure about Monkey Man!

But during the US Civil War the Navy enlisted Young Boys
to look after the Powder for the Guns and they were known as "Powder Monkeys"
Now that the Age to Join the Navy has risen then maybe
the Name has gone from the Boys to the Men in Charge of the Powder and Loading of the Guns.

Answer 3

I believe you maybe referring to what was known {During Nelson's Time} as a "Powder Monkey" : These were usually young boys 11 to 14 years old who were nimble & swift of foot who were employed during gunnery engagements to run back & forth between the "Gun-Powder Magazine" and "Guns" Collecting and Carrying the said Powder to the "Gunners"!

Similary the Slang name of "Nippers" attributed nowadays to young boys also originated from the 'Royal Navy'
As a "Nipper" was a small boy who was capable of entering the confined area of the 'Anchor Cable {chain} Locker Room' when the anchor had been lowered & Secure the Cable {chain}to prevent further cable being allowed to be payed out This was known in Naval Parlance as "Nipping the Cable" hence the Boys who carried out this dangerous task were known as "NIPPERS".