Why would that make you look like a fool? Just do it! If someone questions you, invite them to join it. You might recruit a work-out partner, or at least get someone exercising.
Walking lunges all around the neighborhood, or around the park, etc. If you can find something heavy to carry, great!
Sled-dragging. There's a lot on line about this, including a couple of threads in this forum. Peter Dell'Orto had a home-made sled build out of a couple of old wheels, chained together with rocks or kids inside.
Slosh-pipe. Get 8 or 9 feet of 4 or 5 inch PVC pipe. Cap one end, fill 2/3 full of water, cap the other end. Lift it, toss it, squat it, press it, or just try to walk around with it. I made one, but just had to sacrifice it, cause we can't get PVC pipe very readily (and it's expensive) and my son needed it to pack artifacts (bows, arrows and spears) to take home to the US.
Do you have a kid? Or a niece or nephew? Or a neighbor kid? Or an innocent passerby? Lunges, squats, etc., with a kid sitting on your shoulders, "piggy-back", or giving you a hug face-to-face (if they're strong enough to hang on). There's a video on YouTube of a guy doing barbell complexes, only holding his dog instead of the barbell. A very patient, calm dog. You could do complexes holding various animals, rocks, logs, kids, etc.
Tire-flipping. A classic strong-man exercise. Requires some space. And a tractor tire.
Body weight exercises, like push-ups. You can do feet-elevated to make them harder, even progressing on to very steep and even hand-stand push-ups. Have a partner place a weight on your shoulders, or have one of the above-mentioned kids climb on. You can do chin-ups on bars, pipes, tree branches, beams in buildings, etc. If it's too big to grip, toss a rope or towel over it, and grip the towel or rope on each side. Lash heavy things (or one of the kids) to your body to make you heavier.
Make circuits out of the above. 10 towel pulls, 10 push-ups with your feet on a park bench, 10 walking lunges. Repeat to see how many times you can repeat the cycle in a 10 minute or 20 minute time period. If you go back to the same tree branch and park bench regularly, you can track progress.
I'm sitting in an airport right now. If I were serious about not worrying about looking foolish, I'd work out right here at gate 33. But I'll put it off a day or two, and do it in a "proper work-out place."