You need to oversized one, or get one made for that. Most cold baths that I have seen in locker rooms have 220v chillers.
If you had a small enough body of water, then a normal aquarium chiller might be able to get the water down to 40 degrees, but I doubt that it could keep it there once you put a body in it. This might be OK since you are not in there for long. Ice could get you the extra part of the way. A chiller like this will need vented to the outside since the heat that it pulls from the water will be pretty large and it has to go somewhere.
I do have a lobster tank chiller with drop-in coils that does a much better job than than a typical aquarium chiller. Commercial vs hobby grade.