Youtube videos of mine in which I play Billie Jean are flagged, but still online and shareable.
Vimeo, most likely, but as said they can be taken down there too. It’s just less likely because someone has to actively complain.
Even if you somehow buy web/cloudspace for yourself. The provider for that webspace is also required to react to DCMA requests.
As you don’t want to make any money with it I don’t think you’ll get problems for posting covers online, but your question boils down to: how can I do something that’s not allowed without repercussions for it?
(I even would argue that deleted/taken down videos are hardly any repercussion…)
It sucks, but it is what it is.