No, they wouldn't. Capitalism is driven by supply, not demand.
If by some magic we switched to renewables over night, the owner class would open or expand another market to keep those ships moving.
No, we would have an over capacity of shipping space, forcing the price down sharply. In the short term goods would be much cheaper to ship, reducing in a host of global economic changes- some good but alot not.
The ownership class is not physically capable of doubling our good production overnight to keep them running - long term though its quite probable. Ships will be refitted, a lot scrapped, new orders canceled- but it takes time.
And capitalism is absolutely driven by demand. Any organization that tries to tell people to buy something they aren't interested in will fail. They can alter demand, and yes they control that, but it us demand driven.
It's both. If demand goes down, price goes down; of supply goes up price goes down.
I expect the supply of shipping is pretty stable. It takes a while for ships to be built, it takes time for them to wear out, so in this case demand would be the driver of short term change, pushing the price of shipping in those ships reduced.
I wonder what could be carried in a former coal carrier.