You and I have a similar marriage, it seems, although I'm married to a woman. I've never cheated on her, but she is uninterested in sex and recently told me that I can be with other women too. I'm also insisting on talking with her about it, and she's probably most comfortable if everything is kept very quiet.
I totally get how hard it is on the ego to always be the one initiating, even if your partner does have sex, it's hard to know they probably don't really want to and are doing it to be a good spouse. Being turned down sucks too. There's still a lot of grief in me over the loss of the sexual part of this relationship, which used to be great.
I get the pressure to cheat, and I definitely have thought about it a time or two, but didn't want to do that to her and to me.
What 'glue' do the two of you still have with one another, now that the sex is gone? Do you still want to be with him? For now, my wife and I are very loving with one another, just not sexual, and that's worth keeping. Your mileage may vary. In terms of being truthful, I think it's always best. However, the degree of detail your husband wants about your other partners might be very low, beyond knowing they exist, which seems okay to me as long as everyone is clear about that and you know from him what exactly he does and does not want to know.
Personally, I'd want someone close to me to know when I was on a date or sleeping at another persons' house, for security reasons if not anything else.