ANZ will do 90% and go off the COS but you need to meet a few small conditions. ME Bank sometimes do this as well.
All other lenders will require full valuations at 90% but again all you will need is the executed front page of the COS. Your signature is sufficient - you don't need the vendors...
Most lenders will just require the executed (by you and not the vendor) front page of the contract of sale unless there are special conditions in which they will require the full contract.
Also note that a lot more lenders are accepting COS (no need for valuation) at 80% LVR.