The Henry Beck you are speaking of is probably the same Henry Beck refered to in "A History of Newfoundland" by D.W. Prouse 1895:

In the last French war, before the battle of Waterloo, Mr. Henry Beck, an old Englishman, ancestor of the Becks of St. Lawrence, had his fishing skiff armed. In the spring of 1814 he captured a large French banker by boarding her and driving the crew off the deck. He was taking his prize into Harbour Breton. It was a fine day. The French cook was in the galley getting dinner ready for all hands. An altercation took place between one of Beck's fishermen and the cook. As the vessel was passing Little Cape, the cook threw the contents of the frying pan into the Englishman's face, blinding him. This was a preconcerted signal agreed on among the French crew. They seized Beck's men and threw Beck into the hold, breaking his bones; he died soon after.
The Frenchman took the banker to Boston, USA where the St. Lawrence men were kept prisoners until the autumn when they returned home.

I believe that the Beck families from Swift Current and Sound Island are probably related to this indiviual but haven't been able to make the connection.