During my stay, I was browsing an Internet shopping site for cosmetics and I unintentionally placed an order.

Contact the website operators, explain the situation, and tell them that you did not intend to place the order. Under Japanese law, you may be able to cancel your order if the final confirmation screen is not displayed. If the final confirmation screen is not displayed, and you have not clicked on the "Place Order" button, inform the website operators of this and ask for assistance. If the final confirmation screen is displayed and the order has been placed, the rules stated on the site regarding refunds and returns will be followed in principle. In this case, check the terms and conditions of the site. Note that a cooling-off period is generally not granted for online shopping.