Doesn't work like that. Any NTC is void once a player is dealt, the Oilers opted to honor Visnovsky's NTC but there seems to be conflicting sources on what that NTC actually us.
I've heard the Oilers gave him an NTC, but it was only for like 1 or 2 seasons.
That's not quite accurate either. I believe if a player waives it to be traded, the new team is still bound to it. Visnovsky's case was a little different because he was traded before the NTC even kicked in, and in that case the team has the option of honouring it or not. I can't think of any reason why any team would keep the NTC if they have the option to void it, but you're right that there hasn't been any difinitive reports of what the Oilers decided to do with it.