Only provide 2 options for explicit search
You expect most people to be "not disclosed" - this will severely limit the benefit of any excluding filters, since the majority of your hits will still be "unknown" even if you have a preference when searching.
I would provide a button in the filter-menu called "HIV Status" - if the user clicks on it provide a popup dialog:
Filter by HIV-Status
Some of our users chose to freely self declare their HIV-Status as positive or negative. This declaration is not verified in any way.
- Show only Self-declared positive
- Show only Self-declared negative
- Show all users
Reasoning
The user will usually filter and then search through a list of profiles, where a self-declared HIV status can be displayed. You could even ask on signup "Is HIV-Status something important to you?" and then display the self-declared status more prominently in profiles.
Excluding certain results just sends the wrong message, since most are undeclared, so the filter will most likely have no visible effect for the user and just provide a false sense of security.
Providing an explicit search for self-declared people will give like-minded individuals a way to search for individuals in a similar situation.
Only one Option?
I would even talk to the client if they can change the requirement to only allow declaring HIV-positive explicitly and leave all others unknown. Because realistically you can only be sure to be positive - nobody can ever be 100% sure to be negative.
Negative would immediately lead to more complicated questions: like when was the last test? ... Which is why I would think about removing the option.