Calendar in sidebar

I would like to edit the (widget) calendar so that if someone
is not logged in, and a post is set to private,
rather than going to the ‘You’re looking for something that is not
here’ page, it just reloads the current page (#)

I’d still like the days with posts to be links (highlighted) and
the alt tag to still show the title, just cause the link to be
inactive to the general (not logged in) public.

I’m sure it’s easier than I’m making it out to be, and I seriously
appreciate whatever help can be lent!