Ultimately, yes Masters of the ship (merchant ships most often had just the master) carried some money with them to pay expenses

but for your exact cases situation is more complicated. Crew was usually hired for specific journey and payment was agreed to be done at end destination which often was at return to original port (to make sure your crew stays all trip). Some advance would be given before sailing (e.g. 4 months wages in some exploratory voyages). Payment would then be settled in relative safety and availability of funds in familiar port.

Additionally "banks" would often be involved and instead of actual cash, bank letters of exchange could be given. Not sure how widespread that would be but it was definetly an option to make sure not much cash was carried on the trip itself. If nothing else the master could withdraw cash at the port from a bank if he needed cash for wages.

The same goes for cargo, banking and exchanges were the norm. Just wanted to point out by then there was a separation of shipping and trading so while the master could buy and ship his own goods, he may just as well just sell space on his ship and let others deal with buying and selling goods