Except that dry ice is cold and will increase the CO2 concentration in water. In sufficient quantities, either of which are deadly to fish.

Nitrogen, argon, and various inhaled anesthetics can be used to euthanize a sick bird, but the method we use is C02 in a chamber. The CO2 does not cause distress and is the preferred, recommended method. The AVMA has approved the CO2 method as the most humane, also we are in compliance with AAHA.
Not entirely sure what the rest of your comment means.