I wouldn't do it all myself. The problem is, that once it is thawed, bacteria starts growing. The longer it is at room temps., the more bacteria there is. If you had it warmer than room temps (like most people do when thawing in warm water or under a heat lamp) there is even more bacteria. If you refrigerate it, it slows the bacterial growth, it doesn't stop it. The problem is that there is already a substantial amount of bacteria to start with at the point you refrigerate it, so the bacteria has already had a really good start. (Plus your refrigerator temps. determine how fast the bacteria grow also.)
Your question is kind of like asking, I have some meat that has been in the refrigerator for a week, how much longer will it last?
If it has been at room temps., for say 2 hours, it might correlate to the above question. If it has been at room temps., for 3 hours, it might be more like 2 weeks old. If it was warmer than room temps., it could correlate to a longer period still. It's very hard to say just how bacteria laden it is at the point you refrigerate it.
Another way to look at it is something like this. A certain number of bacteria is in all food. If at room temps., the bacteria doubles every 1/2 hour. At warmer temps it doubles every 15 min. In the refrigerator it doubles every 8 hours.
So if you have a mouse with lets say 10,000 bacteria per lb. and you warm it for 1/2 hour and then leave it in with your snake for 2 hours. You would get 10,000 (doubled 2 timed during the thawing process) = 40,000 and then doubled every 1/2 hour for the 2 hour period it is in your snakes cage =640,000 bacteria per lb. before you even put it into the refrigerator!
Now, instead of warming and putting that mouse in your snakes cage, you put it directly in the refrigerator. Now you have 10,000 bacteria per lb. to start with, 20,000 after 8 hours, 40,000 after 16 hours, 80,000 after 24 hours, 160,000 after 30 hours, 320,000 after 38 hours, and 640,000 after 46 hours.
All these numbers are just made up, but I think you see what I mean. It's probably a lot worse, in reality, than the example I made up. Try that example above leaving the thawed mouse in with your snake for 4 hours and it gets a lot worse! How many bacteria were there actually at the start, what temps. was the mouse at when thawed, exactly how long was it thawed, how cold is your refrigerator, etc. There are just too many variables for me to be comfortable with refrigerating it.
If it was thawed quickly, and it wasn't with the snake too long, I would refreeze it before I would even think about refrigerating it.
Rodney