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."
Glyncoch have had a remarkable past couple of seasons, having lost just once in the last two seasons. Their fine form has been capped by claiming the South Central Division 5 crown of the SWALEC League.
With two rounds of the HSBC Sevens World Series remaining, Wales head coach Paul John has sprung a few surprises for this week's penultimate round in Glasgow. And there's still plenty to play for with World Cup spots on the line.