Wireless router a on plane

No, you may not. Here is United's electronic devices policy, which is entirely standard across the airline industry and just happens to be the first one I found when I searched. It says,

Devices that are NOT permitted for use:

• radio receivers and transmitters

A WiFi router is a radio transmitter, so it is not allowed.

As another example, British Airways says

Any device that transmits or receives communications but does not have a ‘flight safe’ mode, must be switched off for the duration of the flight.

Japan Airlines says,

Please set electronic devices to the mode which do not emit electronic signals or turn them off when cabin attendants request to do so after all doors are closed. Those who break the law may be subject to fine of up to 500,000 yen.

and has a diagram showing that "electronic devices that intentionally emit radio waves when activated" must be switched off between the time when the cabin door closes and after landing. "Mobile routers" are explicitly listed as forbidden at this time.