The hammocks presumably would be made of fairly heavy, undyed canvas. As that material ages (and gets soaked with salt water, rain water, and heaven only knows what else, and dried again) it does take on a dull, greyish, beige-ish color that, as you've noted, does not bang the viewer on the back of the eyeballs like white paint does.
There are a couple of other options. You could leave the hammock nettings empty; lots of models are shown that way. Or you could fit the hammock cloths. Those were heavy pieces of canvas, frequently painted black, that were cut to fit over the stowed hammocks and laced in place each morning when the hammocks were stowed. This is one of the many cases where the approach is up to the individual modeler.
Good luck.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.