I believe you can request the KUL-SGN boarding pass when checking-in at SIN and luggage to be checked through (even though I never tried it).

If for whatever reason they didn't allow it, you can just do the online check-in and print your boarding pass. If you want a printed pass, you can also check with the KUL Lounge or even the transit counter at the Main Terminal.

I remember SIN side couldn't issue me the boarding pass for my separate ex-BKK flight on the same day once, but that was a couple of years ago.