It's the checking-in part, not the printing-out part, that's important. As the PP noted, the front desk at your resort will do your check in for you or you can do it on any Web-enabled cell phone or other device. If you're at a park or at DTD the guest services locations there will do it for you as well. You can just get your printed BP at the RAC desk if checking your bags there (SWA passengers can now use RAC at any resort except for OKW or CBR) or at the airport via a kiosk, skycap or manned counter.
One other option you may want to consider for convenience sake is SWA's Early Bird Check-in service. For $10 pp each way SWA will automatically check you in 36 hours before your flight eliminating the need for you to mess with the process at all while on vacation. You can then get your actual BPs printed the same as noted above.