I don't think your chances are particularly high. The South Korean banking system is quite closed off as there is hardly any demand for KRW outside of Korea. You can try the local banks there but you'll probably need to establish a branch or a subsidiary in South Korea, with 1–2 locals working in an office there.
For what kind of business? Do you mean 200–300,000 USD worth of KRW?
If you plan to receive 3-400 million KRW and convert it to a foreign currency, you︀ can try DBS, HSBC, OCBC, and UOB. You might have to start in SG and︁ HK, and then leverage that relationship to open an account with them in South Korea.︂
That's if it's a low-risk business that doesn't draw much/any attention from regulators.