Wales lock Cockbain was forced to leave the field after being up-ended by Woodcock mid-way through the second half.
The incident was reminiscent of the controversial spear-tackle committed by All Blacks Tana Umaga and Keven Mealamu against Brian O'Driscoll in the first British Lions Test.
But the Welsh management confirmed they would not press for further action after studying footage of the incident.
Coach Mike Ruddock said: "We have looked at the video and spoken to Brent and we will not be citing any New Zealand player. If the independent citing officer decides to do so then that is not up to us."
The annual Women's club launch was held at the Wales Centre of Excellence where National Women's Head Coach and Programme Lead Rhys Edwards, Competition Secretary Adrian Howell and Cardiff Met player Ffion Jones express eagerness for the new campaign to get under way.
WRU TV follows Wales' RWC training squad on day one of their camp in North Wales. The squad were greeted to an official welcome in Colwyn Bay and then headed for an afternoon of team building at ZipWorld