While the currency exchange offices will be closed upon your arrival time, they had a machine right outside the exit into the terminal that will take euro bills and exchange. I can not confirm that this machine is still there but would assume so.
Alternatively you should be able to exchange euros to DKK at your departure airport.
Of course, cash machine withdrawals are available.
I often overnight in CPH without ever taking out DKK and just use my card for everything. Cards are accepted for the train ticket to city, taxis, kiosks... literally everywhere. No need for cash.