I've had to do this while in the middle of the Pacific. Several days before my booking window opened during the cruise I tested out which areas in the ship had the best free wifi for accessing the
DCL webpages. On booking day I went out into the atrium area to use the ships wifi and it was slow, but I was able to book everything with a little patience.
Here's my tips. Know exactly what excursions you want, including second, third choices etc. You will not want to be "searching" on that wifi if your first option isn't available. Also know exactly how to get to it on the webpage, with the slower service you just don't want to be messing around.
Final tip. Don't forget about time zone differences. You will still need to be booking excursions when they open up on USA Eastern time, and depending on where you are, that may or may not be the same time zone you are in. Do the math ahead of time and figure out when you will need to book.
If memory serves me right( and it might not) I wasn't able to do any of it in the DCL app, because I was in "sailing mode" and couldn't switch over to my other cruise.
I was able to successfully handle the challenge of booking excursions while on another cruise. Hopefully you will too!