If it is a vaguely modern WX radar, unless you are hugging the radome with it on for long periods of time you should be fine. The safe distance is about 1.5 metres with a modern unit
AFAIK:
Anyhoo to quote Rockwell collins:
<<RADIATION HAZARDS
To provide a practical safety factor, the American National Standards
Institute has specified a maximum level of 10 mw/cm2 for personnel
exposure of 6 minutes or longer to radar antenna electromagnetic
radiation. The exposure time is limited to the amount of time within the
antenna pattern during each sweep.
In 1980, Collins engineering personnel measured the radiation
emissions of an actual weather radar system on the flight line. A
General Microwave radiation hazard meter (Model 481B) was used to
measure the emitted radiation. It was placed 1.5 feet in front of the
radar’s flat-plate antenna during normal operation with the radome
removed. System range was set to 320 NM to provide the maximum
pulse width. Under these conditions, the maximum power density meter
reading was 0.3 mw/cm2.
In a similar fashion, the United States Air Force’s Armstrong Laboratory
measured the power density of the military version of the windshear
radar and found the highest power density level to be 0.13 mw/cm2.
The Collins WXR-2100 radar system falls well below the 10 mw/cm2
standard. However, it should be noted that there is some disagreement
that the 10 mw/cm2 standard is low enough. Microwave ovens represent
a more public safety concern and their leakage standard has been set
at 4 mw/cm2. The WXR-2100 power density is half or less than that
of the microwave oven standard.
N NOTE
Some sources suggest that any radiation exposure can be harmful,
especially long term. Each airline must make their own decision on
this, as exposure to radiation is occasionally cited by an employee
as a cause of some physical injury.>>
etc.etc. shouldn't be an issue