I'm not going to say that's impossible, but I don't think that's likely. First, the buyout window always starts June 15 OR 48 hours after the Cup is awarded, whichever is later. Now, the latter would basically be something like June 20 at absolute latest, so not too far off from June 15, but the point is it's not a date set in stone. And there could be a situation where a player turns 26 on June 16, and would be able to be bought out at 1/3 if the Stanley Cup was a sweep and it has to be 2/3 if goes to game 7, and I'd imagine it'd be "tough luck" in that situation, since the only wording is age "at the time of buyout". So it's not like something like this couldn't happen in regular circumstances; it's just normally a 4-day window instead of a 4-month window.
I guess they could argue to set the date at the end of the normal buyout window (June 30). So anybody who turned 26 after June 30 can still be bought out at 1/3 in the buyout window. But I'd also imagine the NHLPA would fight tooth and nail over this if it actually came up. And given that, quite literally, Wennberg might be the only player in the entire NHL who turns 26 between July 1 and October AND would be a buyout candidate this offseason, I don't think the owners/NHL would fight hard on this over one guy in a situation that's basically gonna never happen again. (And I also think the example in the first paragraph wouldn't give the NHL much legal ground to stand on here.)