We have cruised with Disney 4 times in the last few years, most recently Dec 2015, and never once have they held our passports. We show them as ID when checking in at the port, and they give them back to us.
I second what other posters have suggested about getting an identification card from your province. I did not drive until I was in my 20's, and the Ontario ID card I had was invaluable for so many things. Also, should you ever lose your passport or other documents, having the ID card can be very helpful in starting the process of replacing things. HOWEVER, the provincial photo card may not be valid for travel purposes -- in Ontario it is "not valid as travel documentation". I don't know what that means in terms of the photo ID needed to reboard ship: you may be able to write to Disney and ask them.
Here is the webpage for Ontario's Photo Card:
https://www.ontario.ca/page/ontario-photo-card Each province issues their own. In Ontario the cost is $35 and valid 5 years.
To be honest, if considering that, for the extra $15, the $50 NEXUS card, also valid 5 years, may be a worthwhile consideration. It is acceptable as travel documentation in some circumstances. It gives you access to NEXUS lines, and US CBP's Global Entry lines/program. It makes you eligible to be chosen for TSA's PreCheck lines, which are usually faster and certainly easier. At Canadian airports that have them, you can use NEXUS lines for clearing security, which are usually considerably shorter than the normal lines.
SW