Can I insure a car that my wife owns and is registered keeper?

You can insure a car that you don't own. However many insurance companies have started to decline quotes where the policy holder (main driver) is not the registered keeper. So you will find it hard to get someone to provide cover for yourself. As far as no claims is concerned, you cannot transfer NCB from one person to another. This is because NCB is a reward that's been given to you for not making any claims to your insurer (no fault accidents) and having the ability to transfer it to another person would defeat the purpose of knowing the risk factor associated with a particular driver.