Wear a kilt.Can you suggest a place to get a medium length cotton one?
If you can'r find a kilt why not wear a cotton longhi as worn by labourers in India (although they wear boxer shorts under theirs.
I have made a video of how to wrap them and can state that if done properly they are perfectly safe for all but the most violent exercise.
The video can be seen here.
I do something similar with a large towel to get the mail or newspaper, take out the trash, or pass from the house to the area inside the privacy fence, but have never felt secure enough to wear it for long periods of active work.
The secret is the large overlap (about 2 feet / 60 cm) combined with the fact that it is folded over at least three times. This is perfectly comfortable with the thin thin cotton fabric but would be very difficult using thicker towelling.
I have never felt secure with a wrapped towel but I feel perfectly OK with the Longhi.
I wear Utilikilts brand. They are a bit expensive at $200, but I find them very comfortable. They can be machine washed, hang dry though. Wear with or without belt, plus the new design has an adjustable waist for slight weight changes. The spartan model is their introductory and it has cargo pockets similar to cargo shorts. I own five personally and wear them any opportunity I get. They can easily be dressed up with traditional kilt hose and a button up, etc. Utilikilts actually have a 10% off products right now. I saw an ad on their Instagram account today.
I assume you mean the short above the knee type.Are they secure enough that they won't fall off when doing active yard work?
Wrapped and folded as in my video they are as secure as shorts.
In order to wrap it securely you should bear in mind that your cotton wrap needs to be about 5 feet by 3 feet for a knee length one on a 34 inch waist.
Edited to add:
I have just made a short video showing that my longhi wrap is secure when worn for reasonable vigorous activity.
It may be viewed here.