What are you expecting to gain by hovering?
Imgur states: "...."
What happens if rather than cutting & pasting the URL you simply hit copy? (And under any circumstances, if you don't want others to see your account page, why don't you upload without logging in? Do you gain anything meaningful by logging in?)
Not cutting and pasting; dragging and dropping as recommended.
Logging in keeps images private; not logging in makes images universally available to anyone accessing Imgur.
Your options appear when you click on
the down arrow to the right of "Copy" (as per the red box), which appears when you hover.
Cut & paste were your words: "I can find a URL but if I cut and paste to address/URL window...." (Doesn't the "Copy" button work?)
I'm at a loss about your "privacy", because I haven't opened an account, but why not use your account for your private stuff and post your public stuff without logging in?
