Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Kuala Lumpur to Košice as you normally would.
Košice Barca (KSC) is the airport you will fly into if you book a flight from Kuala Lumpur to Košice. You should not have trouble finding flights to Barca from Kuala Lumpur; the airport handles an average of 0 inbound flights from Kuala Lumpur per day. You should also have plenty of airline options to choose from since 0 airlines have flights to the Košice airport from Kuala Lumpur. It is only a 5.8 km journey from Barca (KSC) to Košice’s city centre.