Sorry for the lateness, I've been out of town at the
ANS convention.
It seems from my Googling that this name is spelled Hawerchuk, not Hawerchuck. According to a couple of sites, the hockey player
Dale Hawerchuk is of Ukrainian ancestry, so I would assume that Hawerchuk is a Ukrainian surname originally.
According to Hanks & Hodges'
A Dictionary of Surnames, -uk is a common diminutive ending in Ukrainian names. But I am not sure if that suffix is really involved in Hawerchuk.