Hello, if I have a Japanese passport, I can stay in Korea for up to 3 months, and then I can go to landing visa after I arrive in Korea. If you need to stay for a long time (more than 90 days), you need to change it after you arrive in Korea. Or go back to Japan once every 90 days and then go to South Korea.
It is no problem to book a plane ticket directly from South Korea to Japan after plastic surgery.