He? Your husband or his cousin is ex-military?
If it's your husband, then I assume (hope) he has a counselor. See if you can go some time, and bring it up there. You want to be a part of your husband's recovery but, at the same time, your person is being violated. The counselor can be the impartial third party to turn to your husband ask him WTF he's waiting for in terms of talking to his cousin.
If it's the cousin with the PTSD then a part of your 'come to Jesus' discussion has to be to set a date for him to be out and a date for him to get treatment. You are not the man's mother but, at the same time, it would demonstrate compassion (which he really doesn't deserve, but I understand your need to keep the peace) even as you set boundaries and tell him to keep his grubby paws to himself.
Frankly, if my husband's cousin suggested we shower together, I would tell him his next showers while living under my roof would be at the YMCA down the street.