You might want to consider doing full body workouts, as it's harder to find weightless exercises for each body part for 20 minutes.
I've done various things on vacation, without a band:
Yoga (no equipment needed)
squats and lunges (and the more intense 1-legged variations)
push-ups
step-ups onto a chair
sit-down squats on the edge of the bed
planks and crunches
While push-ups work the chest,triceps, front shoulders and the core, they don't do much for the back and lateral and posterior delts. I've used my full suitcase as a weight to do 1-arm rows for back and rear shoulder. I've also done overhead presses with my suitcase.
Since you have a band with you, you can easily do seated rows (for back) and bicep curls, and even overhead presses.
Since you will have access to a pool or water (for swimming), you could do some water resistance moves (A-jock could give you lots of ideas). The nice thing about water resistance is that it works in two directions at once. Like if you do a bicep curl, the biceps are worked on the positive, and the triceps are worked on the negative. An empty water bottle could work as resistance.
Doing kickboxing moves in the pool/lake/ocean? would be cardio as well as resistance.
