In magic the gathering:?

I have a Prodigal Pyromancer equiped with a Basilisk Collar. when i tap my pyromancer to do 1 dmg to something that is like a 7/7 wurm, i understand that normally it would take the wurm to 7/6, but will the deathtouch effect from the collar kill the wurm? and will it beat shroud or indestrucable?