For resistance work, I don’t think there’s any problem with doing the exercises piece-meal. I’ve heard of plenty of people who do pull-ups, push-ups, and sit-ups at intervals through the day. As long as you fatigue the muscles, they’ll get stronger. Normally it’s just convenient to do it all at once.
Working on your feet is definitely a work-out and will help you stay in shape, but it’s doubtful you’ll be working hard enough to get your heart rate into the cardio zone. I doubt it matters unless your goal is to run a marathon sometime down the road. That weekly hike should keep your heart in shape.