Unfortunately, it is sounding like
DCL like other places is expecting everyone to have a cell phone and to be willing to give out the number. My cell phone is my emergency phone with just 5 people having the number, everyone else I give my landline number to. Like OP there are times I don't want to be reachable. I suspect a tablet would work, but is larger than a phone to carry around. On a cruise, all I normally have in my pocket on board is my room key.
I don't know how well the cell phone system works on DCL. I was at Spring Training in Phoenix in March 2020 and at one ballpark that used MLB's app for paperless ticketing. It really slowed down the process of getting into the impact. They are going to have to put some sort of awning or cover over the entrances because the readers could not always read the phone virtual tickets due to glare from the sun, cracked screens seemed to confuse the readers and of course dead batteries were an issue.