Its not possible to fly on an eticket on CPH-LHR with RG and internet checkin is not possible on that route either(atleast not on www.scandinavian.net)

I am not sure if SQ and SK codeshare at all, SQ does have a codeshare number on some flights from FRA to ARN/CPH/OSL but I am not sure if those are LH or SK operated. I am pretty sure that SK doesnt have a SK codeshare flightnumber on a SQ flight.