I mean, you can use 'human' for race/ethnic group, or 'none' for religion, but there's no single word I know of for 'I refuse to state my orientation.'
Yes, I know it's not all that likely to come up in casual conversation, but now my curiosity is piqued.
How about 'exploring'? En passant? Just browsing? Window-shopper? Touchy-feely? Uncommitted? Liberace? Nebulous? Plasma? Spork?
Nothing more comes to mind.
According to my research, 'dick' can mean both a penis and sex in general. Sex in general is mostly a Southern US term and has fallen out of use over the years, but it is still cromulent.
Since the person wants their sexuality to remain hidden, the only logical term is 'private dick.'