The additional shipments aren't going to drastically go up over a few more companies throwing second hand clothing on ships. Large crate ships are relatively efficient for what they tow.

As basic napkin math, if there's 1000 cargo ships moving in and out of the EU in a year, and this law adds 10 more. That's 1% increase. It's a bigger 1%, but I wouldn't be surprised if the emissions are less than the 9% of discarded clothes talked about in the article.

I'm going to speculate that it won't "add" ships at all

As you say, ships are moving in and out of the EU each year - the question is, how many have "back loads" - if some percentage of the ships leave Europe empty to return to Asia for more manufactured goods, then it seems very likely that they can have the containers of unwanted clothes as part of the trip.