I would not delete a log without contacting someone first (certain exceptions apply). If you want to delete it, I suggest collecting your logbooks and looking through to find people who logged your caches but didn't sign. Just because he mentioned it in his log doesn't mean that he's the only one to do it.

If you want to contact him, go ahead. If he admitted in his log that he found it but didn't sign it, how do you think the conversation will go? I'm not sure, but I would guess that someone who doesn't find a cache and decides to log it anyway would not mention that they did not sign the log.
Technically, you should sign the physical log before logging the cache as a find. I have signed all but one cache (in one way or another, some less conventionally than others), with the one exception being a cache so wet that the logbook had basically disintegrated and placing another piece of paper seemed pointless.