A half hour walk is a good start. It should not be a problem wrt keto. Most athletes doing workouts transitioning to keto who burn a lot of calories in a workout struggle to maintain their level of exercise schedule until they are fat adapted. You won’t burn too many cal. this way. However, if this is your intro to getting exercise conditioning might be a limiting factor so build slow.
I’d eat as few carbs as you can for a while and keep protein low. The “nutritional deficiency” will not cause any problems short term. Additionally there are many nutritionally good foods to eat that have high fat content and a vitamin supplement might be helpful. If it sucks while doing it then you know you’re on the right track. “Keto flu” is real and sucks. But it should only last a few days. When you get it tough it out, get electrolytes and plenty of fluid and eat fat when hungry. Oberto sausage sticks, anchovies, mussels, sardines, other beef sticks, pork rinds, etc… Focus on high % fat content. Don’t eat nuts and needless carbs (anything with carbs) while working to get into nutritional ketosis. After you get through the flu something should start happening on the scale. Like @richard has said, if this doesn’t work then maybe you’re the exception in that there’s some other underlying medical condition…