You will still want to bring proof with you if possible:
"
Voluntarily Choose to Provide Proof of a COVID-19 Vaccination
Guests who are fully vaccinated may choose to provide proof of vaccination in order to be exempt from pre-arrival and Embarkation Day COVID-19 testing (unless arriving from outside the United States). The US Centers for Disease Control and Prevention considers people to be fully vaccinated 14 days after the final dose has been administered. Guests may visit the
Safe Passage website by Inspire Diagnostics beginning 33 days before—but no later than 24 hours before—sailing to upload an image file (PDF, JPG, TIFF, etc.) showing proof of vaccination, preferably a vaccination card.
For Guests choosing this option and to be exempt from certain policies on board, it is recommended to bring proof of vaccination (vaccination card) to the port for embarkation. Keep in mind, vaccinated Guests arriving from outside the United States who are required to undergo the rapid test on Embarkation Day will not be charged for the test. Additionally,
travel insurance is not required for vaccinated Guests arriving from outside the United States on sailings originating in the United States."
https://disneycruise.disney.go.com/why-cruise-disney/experience-updates/before-you-leave-home-us/
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