Yes, the information transferred between the base unit (the phone’s stationary unit) and the wireless phone’s mobile unit is transferred as radiowave radiation. Therefore, the “precautionary principle” should also be adopted regarding wireless phones. In addition to the guidelines regarding mobile phones, the Ministry of Health recommends regarding wireless phones:

One of the most robust animal studies in the world comes from the US government. In 1999, during the Clinton administration, the Food and Drug Administration asked the National Toxicology Program (NTP) to study the toxicity and cancer-causing capability of cellphone radio-frequency radiation. At the time, health officials felt epidemiological studies in humans wouldn’t answer these questions, so the NTP embarked on studies in rats and mice.
The 13-country INTERPHONE study, the largest case-control study done to date, looked at cell phone use among more than 5,000 people who developed brain tumors (gliomas or meningiomas) and a similar group of people without tumors. Overall, the study found no link between brain tumor risk and the frequency of calls, longer call time, or cell phone use for 10 or more years. There was a suggestion of a possible increased risk of glioma, and a smaller suggestion of an increased risk of meningioma, in the 10% of people who used their cell phones the most. But this finding was hard to interpret because some people in the study reported implausibly high cell phone use, as well as other issues. The researchers noted that the shortcomings of the study prevented them from drawing any firm conclusions, and that more research was needed.
The energy of electromagnetic radiation is determined by its frequency; ionizing radiation is high frequency, and therefore high energy, whereas non-ionizing radiation is low frequency, and therefore low energy. The NCI fact sheet Electromagnetic Fields and Cancer lists sources of radiofrequency radiation. More information about ionizing radiation can be found on the Radiation page.