Hmm Stranger - if you confirm you have another date then basically you're either saying you don't want exclusivity ('yes I have another date and there's nothing you can do about, pal'), or giving an obvious opening for the exclusivity question ('I do have a date but could cancel if you want exclusivity'.
If someone asks you if you have another date, it's kind of giving the message that they're thinking about the exclusivity thing.
So, if someone asks if you have another date, you've either got to lie or be prepared to say no to exclusivity, which can end things if the other party wants it. Lying about it is putting off the inevitable.
That is all based upon how the question is asked, of course. If it's all earnest then I'd say that's correct. If it's jokey, it could be an opening for him to say he's got other dates too and he has a guilty conscience.
I presume you don't want to have the exclusivity conversation because you don't want it and think he would?