To a certain extent it's your liver over-thinking, and may take some time to figure out what the new normal is.
Say you've just started doing this exercise - you know you will feel stiff for a couple of days after. That's normal, and if you keep doing it, you get a little fitter for that kind of exercise, and fairly soon you don't feel stiff after a session.
It's not just "like" that - it's really all connected. The feeling of stiffness is a process of rebuilding in your muscles, and requires energy. Your liver sees this as extra - new - demand for energy, and so generates a little more blood glucose to accommodate.
And even if it keeps happening, as
@Melgar points out, the benefits of doing the excercise are much greater.
One unique thing about low-intensity exercise (like walking) is that it makes your muscles use that sugar regardless of insulin, so this is why a walk after a meal is so effective.
It doesn't sound like you need to do anything drastic at all. I eat fewer carbs, but I'm reversing a diagnosis - you may be totally fine with what you're doing and eating. The only thing I would offer, is that when it comes to glucose and insulin, there really is no such thing as a good snack. The more time you can give your digestive system off between meals, the better. It's another thing that takes time to become normal, of course - we are all encouraged to snack, and I'm not saying you need to do anything; it's just the simplest way to make the most effective change if you want to.