These things are all paper transactions. For the Oilers to make full use of Sekera's LTIR they need to be as close to the cap as they can be on day one of the season without going over. When they send down waiver exempt guys, it doesn't need to be for any set period of time.
Let's say the Oilers signed Nurse to an amount that would puts them over the cap at ~80.5M
1) Right before the end of training camp, they send Koskinen to the minors bringing their cap hit down below the cap as close to 79.5M as you can get.
2) When day one of the season starts, you put Sekera on LTIR, effectively getting his entire cap hit in extra cap space to use. Once you've done that you recall Koskinen immediately. Your cap hit is at 80.5M but you have ~85M to spend.
I don't think there is anything stipulating that Koskinen needs to be down for the first game of the season. He just needs to be in the minors at the time Sekera is put on LTIR. Since he's waivers exempt, there is no 24 hour waiting period to see if he clears, or anything like that.
Anyways... that's my understanding of the situation. I could be wrong though.
@Fourier would likely be able to give a more accurate breakdown.