Call it leveraging, call it doing what's right by you. Players don't want to remain where they're unwante,d but they do (especially in the case of veterans) typically want control over where they're going.
Practically speaking, there are probably 13 teams that under no circumstances would trade for Fleury.... they are:
Anaheim
Los Angeles
Dallas
Nashville
St. Louis
Winnipeg
Columbus
NYI
NYR
Philadelphia
Florida
Montreal
Tampa Bay
There's no reason to include any of these teams on his NTC... and realistically, if any of them were to trade for him, it wouldn't be a bad opportunity anyways.
So from there, you've got 17 teams that could theoretically trade for you... Detroit & Ottawa are the obvious teams to avoid -- but beyond that, he has some choice. He'd be doing himself a disservice to not maximize the use of that NTC to have a say in his destination.