About the only non-memory item I would attempt is an APU fire. Can't do much wrong there.
Oops
... APU Fire... Memory item now on the 737-800... at least for the carrier I fly for. Boeing changed APU Fire procedure recently from a read and do to a memory.
But spot on about performing a non-memory checklist without the QRH.
Watch and listen to NTSB hearing about the testimony about the ATR-42 mishap in LBB. The captain is asked questions about that same subject.