Shulchan Aruch (Yoreh De'ah 259:1) says that even if you say (as you do in kapparos) "this money shall go to tzedakah," you're allowed to exchange it. So, "spooky ritual" or not, it would seem that it should be fine to exchange that money for other money; at most, you would have to make a verbal declaration of the exchange (like you do when you redeem maaser sheni on coins).
However, you're asking about exchanging the money for a check; that might be more problematic, since the check is not as negotiable an instrument. Rema there mentions that for tzedakah that is to be directly distributed to the poor, the collectors shouldn't exchange coins for something else, "because poor people may come [to receive tzedakah] and there won't be anything to give them." In modern terms, your giving a check to the organization, I'd think, would slow things down as far as what they can disburse to the recipients (because there's the additional time it takes for your check to clear), and I don't know whether that delay has halachic significance.