I think you're overreacting - but it's only natural. I don't think you have anything to worry about; he's being very upfront with you and I think he's right when he says he's treating his male and female colleagues alike. The only thing I think might be a tad worrying is the dogwalking - no problem with that, and at least he's told you - can't you suggest that you join them on the dogwalking sessions - if they happen at present when you're at work, suggest changing the time so you can go with them - say you want to get more exercise yourself and if you join them it makes sense - the dogs get walked, you all get exercise and a mutual chat.
It does sound as though he understands your concerns and is trying to placate them - but I think it takes a woman to understand how another woman might feel.
You sound a happy couple and I hope you both stay that way - there's nothing you've said to suggest that won't be the case, but if I were you I would try and muscle in on those dogwalking sessions!!