I believe that hiring merchant ships was fairly routine.
Merchant ships were usually hired for two reasons - as warships or as transports / stores ships.
In times of conflict it was the norm to hire suitable merchant vessels and arm them; these were usually referred to as 'Hired Armed Vessels' or 'Hired Armed Cutters' etc. This practice continued into modern times - in WW1 and WW2 hundreds of merchant craft were taken into naval service, the smaller craft as patrol vessels and minesweepers, the largest (the big ocean liners) being fitted and armed, and called 'Armed Merchant Cruisers'.
Merchant ships were also routinely hired to act as transports, carrying troops and equipment to far flung places or as store ships, carrying a wide range of material to support/supply troops or ships on foreign stations. This practice continues up to modern times (during the Falklands conflict they were referred to as STUFT - ships taken up from trade), and at this time the Ministry of Defence has a contract with Foreland Shipping to supply six Ro-Ro ships to carry stores and equipment out to the Gulf
(see:
http://www.dunelmpr.co.uk/foreland-photosNEW.html)
I am uncertain of the terms and conditions, but I think that the usual practice at the 'Lady Juliana' period, was to call for tenders by advertising, then contract with ship owners or brokers, the Admiralty paying an agreed price per ton for an agreed period.