I would eat AFTER the walk. You might try doing the walk even before the coffee. Then you will probably not even want the bulletproof stuff and you'll probably want a smaller breakfast.
I find that strength training makes me really hungry. I usually do it before breakfast. If I have some black coffee after, I can curb my appetite enough to put off breakfast until later.
Female, 5'3", 49, Starting weight: 163lbs. Current weight: 135 (more or less).
Starting squat: 45lbs. Highest squat: 167.5 x 2. Current Deadlift: 190 x 3