I worked at UPS for a while, until I had to go back to school.
NEVER ship anything you care about through UPS unless it's next day air!
With that, they take care of it - it might come in late, accompanied by a classic BS excuse (they say it was left at the door at 9:00AM, when it didn't get there until 1:00PM), but it'll almost always get there intact.
UPS and FedEX make lots of profit on their next day items, and they are expensive to refund. They will make sure it gets there.
Now, as for shipping them 2-3 day. There is only one reason I wouldn't do this - TEMPERATURE. Water, food, not a big deal for 3-4 days, especially if the animal is packed with moist materials. The Temperature WILL fluctuate dramatically during shipment. A well insulated box will stay relatively stable over a 24 hour period. Any longer, and you'll have dead lizards.
If the temps are not bad, they could survive. In fact, they probably will. Healthy chameleons are pretty tough. But you cannot prepare a shipment for the temperatures it'll have to endure in a 2-3 day shipment.
If it's not next day air, it means some time in a big UPS shipping truck. These things, on a cool, sunny day, are ovens. On a hot sunny day, bet it'll be 10-15 degrees warmer than surrounding temps. I used to be there when one unloaded - if it was 90 degrees outside, these things would be over 100 inside, and stuffy, cram-packed to the roof.
Any chameleon inside would die.
Basically, in 24 hours, you can prevent too much from changing inside the box with proper insulation and packing. Any longer than that, you lose control of the conditions inside the box, and you never want that.