Is there an inyan to prevent unnecessary pain to reanimated creatures such as skeletons and zombies, the same way there is for those that are alive for the first time?
Having died once does not exempt a living creature from the laws of tzaar baalei chayim. As noted in this overview of these laws, keeping pets is permitted. Pets include cats. Cats have nine lives (or perhaps seven, but anyway more than one). Nothing in halacha says only the first life counts or says what to do in cases of doubt (do you know how many lives your cat has expended already? I don't). Therefore, we must continue to treat animals humanely so long as they are alive, no matter how many rounds they've gone.
The Gemara in Kiddushin (29b) says: ר' יוחנן אמר ריחיים בצוארו ויעסוק בתורה! In other words, if a person has a reanimated being on his neck, he cannot learn Torah. Therefore, it would seem that there is no obligation to protect a reanimated being, because it could lead to bittul Torah.
An additional reason to be lenient is based on the position of the Noda Biyehuda (Yoreh De'ah siman 10) that killing an animal does not constitute צער בעלי חיים. If so, it would seem that the prohibition of צער בעלי חיים only applies to animals that can be killed, but zombies which have already died and are no longer susceptible to death (at least by ordinary means) are not included in the prohibition.