Why do you think your skink has pinworms? I hope you are treating your pet under the guidance of a vet (ie correct parasite ID's with fecal or adult worms seen, being treated with correct medicine, and dosed by weight of skink).
Humans shouldn't be at much of a risk to be infected with a reptile pinworm, as most GI parasites are very species specific. BUT you should be practicing good hygiene and washing your hands after handling, not mixing human and reptile dishes and utensiles, and washing reptile stuff away from human stuff- ect. Practices you should already be doing whether or not you think your pet has parasites
Pinworms are not uncommon in reptiles. They have a direct lifecycle- meaning there is no intermediate host needed. The parasite eggs in the reptile feces are immediately infective. To get rid of these parasites one needs to treat all cagemates at the same time and be vigilant about cleaning the environment- all fecal material must be cleaned up promptly and consistently. It will much easier to do this if temporarily the skink is housed on newspaper or papertowels. If your skink is housed in any bedding that can retain small amounts of feces- your animal will be able to reinfect itself.
As for what to clean with- soap and water is fine. You can do a dilute bleach rinse and air dry to be extra clean. The point is to get rid of all of the contaminated fecal material. Antibacterial soap has little benefit over conventional soap.
Cheers, Jess b