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 WRU's Women and Girls legacy events - #TRY OUR GAME have proved popular this week with current players and newcomers to the game learning new skills and picking up tips from national squad players.
We caught up with Shona and Ellie from the Wales women team ahead of the start of the Women's Rugby World Cup in Paris next month at a recent women's training session to encourage and promote more women and girls to try their hand at rugby. #tryourgame
The Women's Rugby World Cup warm-up clash between Wales and USA proved bittersweet for centre Elen Evans. Despite being one of the star performers on the day on her 50th Test appearance, USA edged home 10-7 at Cross Keys.
Wales completed their Junior World Championship campaign with a victory over Samoa. Team manager Mark Taylor and No 8 James Benjamin reflect on a tournament which saw Wales win three games and lose two.
Wales U20 players Angus O'Brien, Nicky Thomas and coach Richard Hodges are determined to finish their Junior World Championship with a flourish when they tackle the big hitting Samoans tomorrow in Auckland.