If you have a favorite brand of shampoo, shaving cream or lipstick, by all means, bring it with you. Japanese toothpaste does not contain fluoride. Foreign brands do but they can be a challenge to find and expensive. Mouthwash or plaque destroying mouth rinses are available, but again, not cheap. Same for dental floss.
Vitamin supplements are available, but the dosages are small and the prices are big.
Vitamins are worth bringing with you. IF you feel strongly about products that do not harm the planet and were tested without cruelty to animals, bring your own, or arrange to have them sent. If you are worried about being able to decipher the garble on the labels, bring a supply with you. Japanese brands just don't cut it. Heavy duty stain removers are difficult to get, so you may want to bring a powder or stick type.