LG. Two things.
Thing 1: any update on the secret hotmail account? has he said anything? are you going to ask, or let it drop?

Thing 2: Have you considered telling H that it wears on you to continually find his evidence? He complains that it comes up-- but his failure to simply get rid of the junk clearly contributes to keeping the past, in the present. Maybe you could respectfully request that he take an hour out of his life, to clean up after himself? IMO, he is being disrespectful of your feelings to allow you to continually be "taunted" by the evidence, it is callous and cold. I think you should tell him it bothers you, make a respectful request, and then sit back and see what happens.

It would be a very reasonable thing to ask-- in fact, I see it as extremely odd he has not done so one his own long ago. If he will NOT, I think that's pretty telling. At a minimum, I would not put myself in a position to find more junk doing him favors like cleaning out his shaving kit.

Naturally, this is probably totally opposite to your plan, but it wouldn't be me if I did not at least bring it up.