Hugill, "Shanties and Sailors' Songs."
Hugill, "Shanties from the Seven Seas."
In neither does Hugill give the opinion "that the phrase in question means to knock down with a blow,...."
Hugill does mention the strikers and blowers as mates, but does not tie their actions to the chantey.

The true explanation of "blow the man down" is quite simple, and, once heard, is obvious.
On a Blackball packet, the bags of beans got wet in a gale. The mates agreed the beans must be eaten before they went completely rotten.
For two days the men ate nothing but beans. On the third day, their complaining bowels were painfully and noisily demanding relief. The captain ordered all hands to take a carminative, the ship headed into the wind, and shouted "Blow, bullies, blow."
This is the event that is celebrated by the chantey.

There is some discussion about whether the wind so generated was stong enough to "blow a man down," or did the sailors blow up the tale to regale their lady friends ashore.