I was hoping to get some additional information from you, but didn't want you to wait too long for an answer.
It's possible that Skike is biting your wrists occasionally, because he wants your attention and/or wants to play. If he is an only-kitty, he may feel lonely and want companionship, so, if you are his primary caregiver, he views you as a 'littermate' and wants to play.
If you ever use your fingers or hands as toys for him, this might be encouraging him to bite your wrists, so it's not a good idea to do that. Also, if you are petting him and he bites you, he's trying to say 'enough!' because he's becoming overstimulated. If your reaction when he does this, is to scream or yell, it's a negative reaction, but it's 'attention' and he doesn't care if he gets negative or positive attention, as long as he gets attention.
I would recommend enriching his environment with a tall kitty condo or cat tree and a variety of different toys he will like. Here is a great selection of toys:
You can also play with him with interactive toys, like a laser pointer and a feather wand. Just make sure not to leave the feather wand alone with him, as pieces can be chewed off, so only play with this WITH him, under your supervision and then put it in a place that is inaccessible to him.
I would also suggest getting some Feliway plug-ins. These resemble plug-in air fresheners, but have no scent to humans; they emit cat calming pheromones, great to alleviate any stress/anxiety and are available in major pet supply stores, some vet's offices and online.
It's also possible that this is how Skike is letting you know that he's not feeling well, he needs his litterbox cleaned, he's hungry, or trying to communicate something else. For example, if you're speaking on the phone and are gesturing and speaking excitedly, this may make him a little tense/anxious and that's why he will bite your wrist.
When he does this, tell him firmly (not yelling), 'No biting!' and walk out of the room for a few minutes. If you are consistent with this, he will come to realize that he would rather have your company than bite you. Afterwards, you can direct him to a toy to play with.
I hope you found my answer helpful and things will improve with Skike!
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