It’s less about availability, both would be available to Nabataean traders. Linen use in India actually predates cotton.
History of Linen on the Indian Subcontinent
Linen was used in India before the use of cotton, and cultivation of flax dates back to the Neolithic and late period of Stone Age [Dhoni, 1994]. Linen flourished well in Indian subcontinent as it grows well in both the peninsular south and alluvial soil of the north.
Cotton one of Egypts Most Famous Exports
Also Cotton had been grown in Egypt since 3000 BC.
Nabataean sailing ships dated from the 6th century BC and did not share the same criteria with the 19th century ships which would select cotton when given the choice of linen. Such ships which choose cotton over linen were an exception to the rule prior to the introduction of steam ships. With both cotton and linen available to Nabataean sailors the choice is clear which would be preferred for the kinds of ships the Nabataean traders favored. Smaller ships, with simple rigging outfitted for long haul cruising. For longer voyages linen was preferred even if it had to be purchased at a premium. Linen simply had superior properties for long haul cruising, even if for racing cotton would be superior.
This is actually a perennial question for sailors which is still topical today. Balancing durability and strength with performance, be it cotton vs linen per your question, or Dacron vs composites the choices for today. The materials change the decision criteria doesn’t; lighter less durable materials are superior for racing, but heavier more reliable materials are more valued for long haul cruizing.
Both Cotton and Linen make poor sails by modern standards. They both absorb water, rot in UV light, and are highly subject to mold. Linen is stronger. Cotton is lighter. By stronger there are two meanings. It lasts longer without tearing and more importantly holds its shape better without stretching. Tears can be sewn but stretched sales need to be replaced. For reliability And predictability Linen was the preferred material even when more expensive, even when cotton was more readily available. Linen was preferred over cotton during the age of sailing ships, if there was a choice because it was more dependable, lasted longer and perhaps most importantly was more predictable when eroding. If racing durability took a back seat to weight. For new sails cotton performed could perform better than linen, stretching wasn't a problem as the sails could be replaced at the beginning of each race, weight was the primary concern.
Cotton only replaced linen as the preferred fabric in the 19th century for two reasons.
(1) sailing ships got so sophisticated with so many sails linen just became to heavy to manage, too time consuming to lift. Nelson’s flagship HMS Victory has 37 sails or 4 acres of surface area in 1780, By 1850 a similar ship with then more modern rigging might have more than 100 different types of sails to take advantage of different types of weather and wind conditions.
(2) Cotton as a preference over linen was especially pronounced after the age of sailing was concluded, when practicality took a back seat to performance as sailing ships ceased to be vehicles of war and commerce and became pleasure craft and status symbols.
Still every ship which can float linen can float cotton sails. So if it were a necessity cotton would do, and sometimes it was a necessity.
During the age of sailing(the mid 1800s) cotton was used in cruising ships (merchant and military) mostly when linen could not be had at all.
If you look at the United States which was the largest producer of cotton; linen which depended upon imported flaxen, was still the fabric of choice for sails. In US merchantman and war ships, cotton was only used when global affairs conspired to make linen unavailable. Like the war of 1812. But once linen became available again it was used again. Cotton didn’t surpass linen on ships until after the steam ship pushed sailing ships out of the worlds navy’s and merchant fleets post 1860's.