1. Carve edible shot glasses from melons.
2. Use spare egg cartons as shot trays.
3. Stock up on flavored ice.
You can't go wrong with coffee, tea, watermelon-flavored juice, and so on. Well, you could, so it probably wouldn't hurt to try a small batch before your event.
4. Even better: oversized cubes.
Use Tupperware or a gallon bag — something that will expand without breaking or that you won't feel bad about cutting into to get to your cube.