Did Age of Sail fighting vessels have any anti-spall technology?

The introduction of hammocks in place of cabins for the bulk of the crew both reduced the amount of wood (and thus splinters) and led to the use of rolled up hammocks as protection against splinters. Canvass and bedding were also used. Although this mitigated the problem to some degree, it was often ineffective and there was not much else they could to protect crews from splinters. (see testimonies near the end of this answer)

On the problems with cabins,

A young boy recalled his experience in the cabins as “a thing much like some gentleman’s dog kennel, for I was forced to creep in upon all fours, and when I was in and set upon my breech, I could not hold my head upright.” Additionally, sources described them as “sluttish dens that breed sickness in peace, serving to cover stealths, and in fight are dangerous to tear men with their splinters” and “nasty holes, which breed sickness.”

Source: Michele Panico, 'Hammocks: A Maritime Tool' (2018)

The change to hammocks by the Royal Navy from the late 16th century was not (apparently) primarily because of splinters:

The answer to all these problems came in the form of the hammock. Health factors, it seems, most heavily drove the transition. Several officers and medical professionals advocated for the switch to hammocks.

Source: Panico

Hammock netting didn't just help protect against splinters:

When filled with rolled hammocks, the netting created a barrier, described by many as a wall, bulwark, or parapet. This primarily protected sailors against musket balls, flying debris, and splinters; splinters being one of the most deadly dangers in battle. It dampened the impact of exploding shells and could even help in slowing the force of a canon ball. Many authors have likened stored hammocks to sandbags.

Source: Panico

Further,

Several captains, such as Captain Hutchinson, went so far as to run a second tier of hammocks above the hammock netting, prior to combat, for the better protection of their men.

Source: Panico

Canvass and bedding could also be used:

On deck, hammocks, bedding, and spare canvass were bundled into the nettings along the sides of the railings to serve as some protection from small arms fire and flying wood splinters, as well as to deter boarders.

Source: Dorothy Denneen Volo, James M. Volo, 'Daily Life in the Age of Sail' (2002)

In many, if not most cases, the protection was clearly limited, though. Below are some first-hand accounts of what happened to hammocks in battle:

On August 2, 1798, Captain Edward Kirby stated, “almost all the hammacoes [were] cut to pieces.” Another Captain, Davis Donaldson, wrote in his log, on October 21, 1805, that “the gangway netting and hammock[s] [were] completely shot to pieces.” A midshipmen explained his personal quandary to his mother on November 22, 1805, "my hammock and bedding had likewise been shot away in the action, which is the more unfortunate as I can so ill afford to replace them.” Commodore Macdonough observed after a battle, on September 13, 1814, “there were not 20 whole hammocks in the nettings at the close of the action.”

Source: Panico

As noted by Steve Bird in his comment below, another way of trying to limit the damage caused by splinters was to remove anything that could be source of such splinters, though the main aim of this was actually to keep the deck free of impediments during the fight. Among other preparations for battle,

Below decks, the partitions that formed the officers' cabins were removed, and the furniture, mess tables, and any other loose objects were stowed away.

Source: Volo & Volo

Ultimately, though, the surest way to reduce causalities (from splinters or other) was to disable the enemy as quickly as possible by improving both tactics and the performance of gun crews. From the late 17th century onwards, this was something the Royal Navy proved remarkably successful at.