IMO that's a major waste of of money and life. If it has only been thawed for a short amount of time, there will not be significant bacterial or other microorganism growth.
In my lab we euthanize mice, perform dissections and biochemical analysis over the course of an hour plus, without any significant bacterial contamination issues. An intact organism can withstand contamination even longer. Adaptive and even intrinsic immune system is still somewhat functioning even in a dead animal. I routinely isolate living T-cells and dendritic cells from the brains of mice that have been dead over an hour.
Seal the mouse, deep freeze and try again another time.