Parasite + Wyrm combo - is it an insta-killer?
Yes, this combo works.

Parasite will trash any ice as soon as it has zero (or lower) strength, regardless of how that strength was lowered (i.e. it doesn't only trigger from Parasite's counters).

Other cards that combo with Parasite include Datasucker:


  Whenever you make a successful run on a central server, place 1 virus counter on Datasucker.
  Hosted virus counter: Rezzed piece of ice currently being encountered has -1 strength until the end of the encounter.


or Ice Carver:


  All ice is encountered with its strength lowered by 1.