I am really hesitant to reply on this subject, since it could be considered medical advice, and I am not licensed to practice medicine. I can give you advice about knots, but practicing medicine should be left to the professionals.
I think what you are looking for is a knot that takes the least amount of space, and that means the fewest turns around the subject. A single turn around the subject will leave you with two choices, and Overhand Knot, or variant, or a Truckers Hitch, or variant. I wouldn’t trust the overhand knot to have lasting hold, even if you tie a second Overhand Knot, and turn it into a Square Knot. The Surgeons Bend might be considered, but you won’t have the option of adjusting the tightness of the knot after you have tied it. The Truckers Hitch can get kind of lumpy, and may also be subject to hold issues over time.
The next smallest knot would be two turns, which is like a Clove Hitch, and variants. One variant of the Clove Hitch is called the Constrictor Knot. This is where you add an overhand Knot under the middle part of the knot, and when you pull the ends, it will tighten snugly, and it will be extremely difficult to untie. Below is a picture where I have blown up a detail from a knot board I made. This is some Three Strand Coach Whipping that has been terminated with a Constrictor Knot on the left, and a Clove Hitch on the right. Both would be suitable to be used as a ligature, but the Constrictor Knot would have much better staying power where the knot might be subject to being worked, or stressed.
I have used a constrictor knot for many years in different applications, and I have never seen one come loose when I didn’t want it to. Unlike a Truckers Hitch, where you have to pull against the subject being tied to tighten the knot, with a constrictor you pull the ends in opposite directions with the knot in the middle. Where I have used the Constrictor Knot as a permanent installation, I have been able to cut the ends very close to the knot without the knot coming undone.
Having not read any literature on the use of a ligature in this fashion, if you do need to tighten the knot in the future, and you leave yourself enough ends to grab onto, you will be able to continue to repeatedly tighten a Constrictor if the subject becomes smaller.
Pat