Yep!!! You can wait to use the Paid Cosmetic BP on a Season you like better and prefer the Cosmetics of. The rest of the Season is part of the game you already paid for. Season Journey, Battlepass with some cosmetics and the Season buffs (XP boost), etc are all part of the base game. Only the cosmetics are paid, and you can use that on whatever Season you want.
In fact, I am sure some will be confused that it is not automatically activated an they have to go to the Shop and intentionally use it.
If you purchased the digital Deluxe or Ultimate Edition of Diablo IV and want to redeem your Battle Pass for this Season, navigate to the Seasons section of the Shop and select the option to activate your Battle Pass.
I think everyone wants the giant tick, Kotick, gone. The part about making good memories with friends is bittersweet. Sort of like trying to recapture childhood. I wish you luck doing that. It is like chasing ghosts to recreate lost memories and times gone by.