The opening encounter between the sides at the Aviva Stadium in March was a fiery occasion that saw Ireland captain Seamus Coleman suffer a broken leg following a robust challenge from Wales defender Neil Taylor, who was sent off for the tackle.
"Obviously we know it is a derby, but we must not get involved in anything," Ledley told Sky Sports News. "We need to be clever and we have a lot of experience, so it is down for us.
"Monday will be a battle and they will fight hard, it is always the same in these games. But it will be a great occasion, and hopefully we can do it with one last push."
Both nations can still qualify automatically for next year's finals in Russia, although they are relying on group leaders Serbia slipping up at home to second-bottom Georgia.