as you probably know, these two constructions differ in aspect. "Budu končit" is imperfective and "skončím" is perfective. But that itself doesn't determine whether you will have successfully completed something or not. Your sentences are correct but their meaning is very neutral. When it comes to perfective aspect in Czech, the prefix is key. That's the part that really carries the meaning, or its small nuances.
In this case, I would say "V květnu dokončím studium." Because do- implies I will do the very last bit that's left in order to complete/finish something.
"Počkej, ještě dojím oběd."
"Kdy už Petr konečně dostaví ten dům?"
In official documents, you can also see "zakončení studia". "Zakončím studium" means I will do so successfully but it's very formal. "Dokončím" is more suitable for day-to-day use.
Hope this helps.