This situation sounds unlikely from our experience. If you have the Shinhan account number, you can make a transfer directly to that account from anywhere. In fact electronic banking is very common in Korea. Your name would appear on the transfer information that the university would see. The transfer can be made from your bank in Finland in KRW.
Not sure who at the university would have told you you cannot make an electronic transfer or that payment can only be made by someone in-country. You can contact English speakers at Shinhan Bank for more details. See here:
http://www.korea4expats.com/service-Shinhan-Bank-Seoul-Global-Center---Banking-for-Foreigners-Downtown-Seoul-919.htmlYou can contact the Shinhan customer service English staff if you need more information. Shinhan Bank English Call Center at 1577-8380 (+82-2-3449-8380 from overseas) for assistance. The Call Center is open Monday - Friday from 9 am - 5 pm (Korea time).
There is an inward remittance fee of W10,000 that you should add to the sum you are sending.