Unless it was powerful enough to cause damage through heating or immediately shock you.
About wireless charging
For most cellphones, wireless charging is done according to Qi or PMA standard:
Whereas the Qi standard works over the approximate frequency range of 100-200 kHz, the PMA (Power Matters Alliance) standard delivers up to 5 W over almost twice that frequency
The used frequency belongs into Low Frequency band. Low Frequency band is included in Intermediate Frequencies. Guidelines don't seem to focus on this frequency range very much. Everything relating to "Low frequency" I found was about "Extremely Low Frequency" (power lines).
World Health Organization on Intermediate Frequencies
For the purpose of this document, the intermediate frequency (IF) region of the EMF spectrum is defined as being between the ELF and RF ranges; 300 Hz to 10 MHz. A relatively small number of studies has been conducted on the biological effects or health risks of IF fields
Research about health focuses on other EM frequencies
I'm using less reliable links here, because it doesn't relate to wireless charging. The links are also more general, just to explain where some of the scary claims about EM frequencies would apply
Within RF (wiki):
- Ionizing radiation (causing DNA damage and cancer) or intermediate non-ionizing that still produces some ionization (wiki)
Health effects of Low Frequency radiation
World Health Organization talking about Low-frequency electric fields (added highlighting):
Heating is the main biological effect of the electromagnetic fields of radiofrequency fields. In microwave ovens this fact is employed to warm up food. The levels of radiofrequency fields to which people are normally exposed are very much lower than those needed to produce significant heating.
So, the main problem would be heating. But it probably isn't heating.
The heating effect of radiowaves forms the underlying basis for current guidelines. Scientists are also investigating the possibility that effects below the threshold level for body heating occur as a result of long-term exposure. To date, no adverse health effects from low level, long-term exposure to radiofrequency or power frequency fields have been confirmed, but scientists are actively continuing to research this area
And if it's not heating, it probably isn't harmful.
World Health Organization on Intermediate Frequencies (added highlighting):
Except for medical diagnostic and treatment devices, levels of human exposure from IF devices normally fall below limits recommended by the International Commission on Non-Ionizing Radiation Protection (ICNIRP).
While strong fields in the upper IF range may cause thermal damage (a relatively slow process that requires tissue to be maintained at high temperatures for a given period of time), some of the most obvious hazards from acute exposure to electric currents in the body may occur through membrane excitation. This non-thermal mechanism results from changes in membrane potential induced by external fields and occurs, for example, in the stimulation of peripheral nerves and muscle cells. Another mechanism is electroporation, which is the reversible or irreversible disruption of cell membranes when a field induces excessive electrical potentials across them. This can provoke tissue injury through electric shock
Unless you are immediately getting shocks or automatic nerves firing.
By analogy, we are in the 1950s of the tobacco industry, with ads extolling doctors?
They only successfully bought TV ads with doctors. Analogy is implying that they successfully bought peer-reviewed journals and scientific consensus.
Is this really a "Class 2B carcinogen"?
Yes, World Health Organization talking about health risks associated with mobile phones and their base stations (added highlighting):
RF fields have been classified by the International Agency for Research on Cancer as possibly carcinogenic to humans (Group 2B). Studies to date provide no indication that environmental exposure to RF fields, such as from base stations, increases the risk of cancer or any other disease.
AAAS criticised WHO's bad explanation of the terminology in Cell Phones Offer Lessons in Risk Communication:
"That classification represented “the weakest result they could come to,” without clear evidence to disprove a connection, Gray said, yet the terminology may confuse people.