A few things:
1) the Canes CAN trade Kotkaniemi whenever they want. The restriction for not trading him for a year is ONLY for a team that matches an offer sheet, so had MTL matched, they could not trade him, but there is no restriction in the CBA that prevents the Canes from trading him, should they want to. Was discussed earlier in one of the threads. (EDIT: and I see two others beat me to it).
2) There are some players, should they not be performing well, that the Canes could move to make space. It may cost something to do so, but it can be done.
3) Every year teams with cap concerns find a way to add when they need to. Sometimes it involves a 3rd team that gets paid to take cap space.
So YES, the cap space would look differently without KK. What we don't know is how much because the Canes were going to add another top 9 forward one way or another so it wouldn't be the full amount. Of course the closer one is to the cap limit, the more maneuvering they need to do to make deadline acquisitions work, but they usually do.