Those share buttons are trackers themselves. So it’s not about “supporting” those websites by publishing content to them, it’s about undermining the privacy of your readers and doing the opposite of what you preach, and “supporting” those websites by feeding them much more valuable user data. As another comment said, just put a button to copy the permalink and let them paste themselves if they want to share.
As for you sharing a link on the mainstream social media platforms yourself, I’d actually encourage that. Cory Doctorow auto-publishes links (not content) to his articles on as many social media platforms as he can (sorry, can’t find the article in which he describes it). The point is that he still retains control over his content by hosting it himself, he controls the (lack of) trackers and ads, and gaining traffic from these platforms is still to his and his potential readers benefit. Bending your rules a little to reach more people and maybe even convert them to be more privacy-aware is fine.
How about… the tanks could be empty?