There is another, easier way. It's more a replacement than update but it works fine. You can create new image style based on the old one but with new features (image actions) you wish. Then delete the old style - on the deletion confirmation page you will find a droplist with avaliable image styles which you can use to replace the old one. This is a standard image style replacement function I assume.

There is another, easier way. It's more a replacement than update, but it works fine. You can create a new image style based on the old one, but with new features (image actions) you wish. Then delete the old style; on the deletion confirmation page, you will find a drop list with available image styles, which you can use to replace the old one. This is a standard image style replacement function, I assume.