You'll probably have experienced this already as you may be travelling while I'm typing this. I don't know if WY agents can check you in for SQ, I would rather doubt that. They can check your luggage through of course.

This issue with online check in when there is a OAL in front of the SQ flight(s) is nothing new unfortunately. I had this even with LH flights prior to SQ ones (all one PNR, e.g. tix issued by LH) and I had to check in at the airport / or get my BP at the gate (or a transfer desk).

I'll have an itinerary next year that is SQ-LH-LH-SQ and there is a gap of a week or so between the last LH and SQ flights. I'm hoping that the gap may be enough for SQ check in function to assume that I have flown the prior LH segment and allow me to do OLCI then, but to be seen. For a "through" connection with OAL prior to SQ, it never worked for me. YMMV.