In NSW most vendors will accept a faxed copy of the contract on exchange provided the original follows within a reasonable time. The solicitor/conveyancer can sign the trandfer for you but you will need to sign the mortgage & loan agreement between exchange & settlement.
Is FIRB approval involved?
If your solicitor/conveyancer does not allow the transfer in small amounts, you could pay the funds to the Agents Trust account before settlement & they can have a bank cheque at settlement. The deposit can be more than 10%.