PeteE.
Whether you need a small saw for the field or not depends on whether you intend to open the chest cavity fully or leave it closed until you get home. The main advantage of leaving it closed is that it reduces contamination as you extract the carcass.
Over here (North Florida), its more important to cool the carcass down, than to worry about contamination. Often during hunting season, the temperature will top 90F.
I use several wraps of cheese cloth to keep the critters and dirt/brush out, but the chest has to be opened for cooling.
