Mate, I would pretty much say its a bit dangerous to start doing core activation after a couple of uni lectures. TVA activation sometimes needs to be taught after LB injuries. To get it right takes 1 on 1 tuition in a rehab setting. Trying that in a group of rugby players would be ineffective in terms of core activation.
As the guys have said the act of doing the wrestling will serve as a core exercise and give you the desired training effect.
Because of the limited time you have to train as an amatuer I would suggest you do game related stuff that covers both the skills and the fitness side of things. Use your knowledge as player and put in some fitness principles and the boys will love it. Carry out some tyre flipping with the forwards straight into line out drills or scrum machine and then back onto another element of the game.
Good luck!