You are doing SouthWest, so you will want to do check-in at Exactly 24-hours prior to your flight, as you probably know. (We delayed 15 minutes while at the hotel after our cruise, since we flew out the day after, and it cost us a LOT of numbers.)
So, if you want to do the normal check-in process, what you will have to do is use the ship's Wi-Fi. If you sign up for the free 50 MB the first day, and promptly sign out of it and don't use it all week, it should available for you on the last day, or you can pay for some. Trouble is, the ship's Wi-Fi is spotty and not the strongest, so it is hit or miss if you will have a decent signal at exactly the right time to sign in. This was the situation that my Sister and her family was in when they cruised with us, since they were flying SouthWest on the day of their cruise, like you are. Thus, so as not to chance a bad sign-in number, she bit the bullet and paid the extra $15 a person to get the "advanced" check-in or whatever they call it. Thus her family could sit together. She did the regular check-in for the flight at the beginning of the trip.
Depends on how badly you want to sit together.