Well, you can't complete the quest without killing him. Your only option is to ignore the quest and leave it uncompleted.
Too bad you're on console, on PC there would've been a mod for that issue. Coincidentally the name of that particular mod is "Paarthurnax Dilemma".
The quest should disappear from your log after you complete the Main Quest. But beware, speaking to the Blades will cause it to reappear (at least it did that in my game).
If you have an Xbox One/PS4 the enhanced version of Skyrim will be released in less than two months. The consoles will be getting mods. I do not know when PS4 will get mods since they still have not gotten mods for Fallout 4.
On every character I play I ignore the blades when they as my to kill Paarthurnax. The blades are not required beyond that point (except for roleplaying). If you do kill Paarthurnax you can no longer talk to the greybeards (who are helpful in finding word walls).
If you're one of those people who must complete every quest, you'll have major problems with Skyrim, as there are quite a few instances of being unable to take both paths. You can only complete one side of the Civil war, to take the most obvious case.
You'll have already failed a quest objective, as you can't retrieve the Horn of Jurgen Windcaller from the tomb, but must get it from Delphine. So just treat Paarthurnax as another of those "must fail" cases.
We do now... never. http://www.gamesas.com/topic/1606602-ps4-mods-officially-dead/
I had a feeling it was going to happen back in June when Bethesda had the PSA that mods are delayed with no ETA, especially with Sony coming aboard kicking and screaming after Microsoft stated they will be allowing mods. I do not think Sony ever wanted mods.