Is it possible to buy out the event shop without apples?

Not without full CEs and proper servant team planning. Realistically though you only really should need to buy the fous, the ascension materials that have low droprates and the gold class monuments. Scathach and her ascension materials are optional tho I'd recommend buying them coz shishou is the best <3. And everything else, silver tokens, the more farmable materials will be available to farm during lulls between content like we just had preceding this event.