Add search passwords by a hash value
Let users use pre-generated hash values to search. Yeah, I know you calculate hashes of typed passwords on a client side, but some people still prefer not to type their password on 3rd party sites.
You can, either works
I can certainly understand a reluctance to enter passwords on third party sites, but it becomes a matter of who you trust. People enter passwords online all the time, and HIBP is a secure site. So, as long as they are not storing passwords in the clear, I don't see a reason to be concerned.
Besides, I'm going to assume that the hashes generated client-side may contain a "salt" value and therefore, any hash entered manually by a user (without knowing the salt value) is unlikely to match what's in the HIBP database.