Hi there Trinity,
Welcome aboard.
You don't need to exercise to lose weight. You don't even have to give up cake necessarily. And although it isn't maybe as easy at 48 as it was at 28, it is absolutely doable.
My advice is to figure out based on your age and gender how many calories your body needs to maintain the weight you're at right now assuming that you are completely sedentary. There are lots of calculators online to help you do that.
Take in less than than that and you should start to lose weight. Or you can do trial and error if you're not inclined to count calories. By that I mean cutting back portions until the weight starts to shift. Or you can use a program like WW or Atkins that gives you a prescribed eating plan that should help you eat at a calorie deficit. Make yourself an experiment of one to find our what works for you.
You're right in that stopping a diet, whether it's a Dukan or any other, usually means a return to old eating habits and a regain. Any way of eating ( WOE ) that you can't follow and enjoy for a lifetimes is likely to fail.
I can't really give any advice on what to eat not knowing what your tastes are, but what I can tell you is that in my experience, nothing's off limits, not even cake. ( Bearing in mind, of course, that some people truly can't eat some things, i.e. diabetics, those with celiac's, etc. Also, some people feel certain foods are triggering for bingeing, so they abstain. )
My motto is I can have whatever I want, just not as much as I want whenever I want. It comes down to deciding how to fit what I want into the boundaries of what my body is able to burn off.
Hope that helps! Good luck with the surgery.