You need an ETA for Saint Kitts and Nevis if you have a South Korean passport
Visa options for Saint Kitts and Nevis
Electronic travel authorization
Travelers need a travel authorization to visit Saint Kitts and Nevis for Business or Tourism. Visa-exempt visitors entering Saint Kitts and Nevis must obtain an Electronic Travel Authorization (eTA). Travelers can submit the eTA application online. Once the application is approved, travelers receive their eTA confirmation electronically. If travelers receive a new passport, they must apply for a new eTA.
This is not offered by sherpa°.
Apply on the government site.