Hello all, new to this site and my very first post - figured I would chime in as I have direct experience on this topic.
My family and I, 2 adults and 2 children (7 and 9 years old), just got back from the Disney Dream sailing 9/13-9/17
Disney adjusted the dates for the 1st test, it used to be 5 days now it's 3 days prior to sailing. With the cruise sailing on Monday 9/13, that put us at Friday 9/10 for testing. We opted for free testing through CVS (book as early as possible), and made drive-up testing appointments for the kids after school. After paperwork and preparations, the entire process took about 30 minutes. The tests are self administered and you only need to stick the cotton part of the swab into the childs nose, my kids were not uncomfortable at all and thought the cotton tickled. The results were ready the very next day (Saturday) via email. I cannot thank CVS enough on how easy they made the process.
Now on to embarkation day - as you pull up to the parking garage (and after paying) you will be guided to a testing area before parking or leaving your car. It's at this point that everyone sailing, even if vaccinated, will need to test. Just like everyone else, we were nervous about our children testing. And just like CVS, the cotton swab only needs to clear the nostrils. These tests are not the kind that poke your brain! literally only goes in about as deep as an adults thumbnail. A super quick and painless process. After testing, you will drive up to an empty parking spot where you stay in your car and wait for the results of the tests via email or Safe Passage website (I was refreshing constantly). After about 45 minutes we were given the all clear to board!
Hope this helps any new cruisers.