I have an itinerary booked from ZRH-BKK-SIN, on TG and SQ. I am really starting out that day in AMS, and I need to purchase a separate ticket. If I buy from KL (which is cheaper), can they check my bag through to SIN? I should really fly on LX (since they are in Star Alliance), but the KL ticket is cheaper. Both allow for ~4 hour connection in ZRH.