Whilst not defending your husband's laying down of the law, there are security issues with Skype. katerussell.co.uk/essentials-skype-security-risk/ has a fix down the bottom to better protect you, suggest you print off the article, show it to him, and offer to put the necessary tick in the box?
Nothing is truly safe online these days, we all have to do our own risk assessments. Without wishing to be alarmist, I am far more worried about the data collection from Facebook 'likes' and Twitter postings, which along with your Google searches can build up a far more accurate profile of you than perhaps even your spouse is aware of! - and these profiles are sold on, or used to manipulate what you see online. There have been suggestions that this was how the American election was swung, I couldn't possibly comment. 
If you don't care what the world knows about you, then there is no reason to worry, and the younger generations certainly will just accept the lack of privacy, it doesn't bother them. It is only us oldies who want to haul back on the reigns.