Do what you want, but that's not how that works. Businesses aren't "using" or "taking" your donation or claiming them as their own. They're basically just serving as a collection point for whatever charity indicated. If you choose not to claim it yourself, that's your choice, but the donation is "from" you "to" the charity. The supermarket or whatever just provides visibility for the charity and the collections logistics. It saves those charities having to find people to stand outside and ring a bell and hope you have change in your pocket.

If you're not contributing to a charity in lieu of not participating in these "round up donations" programs, then you're simply choosing to not donate to charity. Which is fine, as far as that goes.