I don't think you would need to leave it ambiguous. The Federation has gone past the need for a monitary economy (though they do use 'credits' and there was the Bank of Bolarus), but private businesses and enterprises would still work with some form of payment (The Tigan mines were still very concerned with balancing the books and had money to pay Mrs Bilby).
Anyone who would head out on a venture such as this would be leaving the UFP and their system behind, they would therefore need to adapt to the economy of the area and work with latinum or whatever currancy was used. They would need to cover the expense of fuel, crew, supplies, repairs, docking fees, bar bills and whatever other costs arose. All of which I would think would fit in better with a 23rd century setting, when the universe was still a little more uncharted and Starfleet didn't seem as expansive as it was by TNG era.
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)