I was at SPL today and went up to the Transavia/Viggo service desk in departures 1, landside. I first asked if there was a transfer desk airside, the answer was no. When i explained the issue (possibly not having a boarding pass for the connecting Transavia flight, coming off a flight from the UK on KLM), the agent immediately said: in that case, go straight to the gate of departure to Sevilla and get your boarding pass there. No doubt in her voice. So this must all be reassuring for you, and, like several posters in this thread, i think you will be all set in LBA with boarding passes for both flights. Enjoy your flights