Batteries have two kinds of radiation. One is that the battery contains trace radioactive elements, and there will be a very small amount of ionizing radiation, but this can be basically ignored (normal people also contain radioactive isotopes such as hydrogen isotope deuterium and carbon isotope carbon-14, so the human body will also emit slightly cold ionizing radiation, but the order of magnitude is similar to that of the battery).
And electromagnetic radiation. Because the battery temperature is room temperature, which is higher than absolute zero (-273. 15 degrees Celsius), it is more physical. As long as the temperature exceeds absolute zero, the object will radiate infrared (an electromagnetic radiation), so the battery will also radiate electromagnetic waves. However, because the human body temperature is usually higher than that of the battery (the body temperature is 36.5~37 degrees Celsius), the electromagnetic wave intensity radiated by the human body should be higher.
Also, because the air is not absolutely insulated, there is leakage current around the battery. The periodic change of leakage current in space will excite electromagnetic field and produce electromagnetic radiation, but this value is about tens of thousands to millions of times that of surface electromagnetic wave clutter. Even a very professional instrument with high sensitivity depends on luck.
So to sum up, the battery has radiation, but it is completely harmless to people. I don't care at all.
I hope my answer can help you!
You're welcome.