Is there a risk?
Sure, there is a risk of damaging the Pi unless you know what to do and do it right using the appropiate equipment. Personally I would say that it can be done with basic soldering skills and a little experience in soldering electronics. After all the RaspberryPi Foundation shipped the early Pi Zero without the pin header and considered it safe for hobbyists to solder that themselves. The thermal load (again, if done properly) should be about the same if desoldering an existing pin header
Some other opinions though:
... and as an alternative to soldering:
What's the best way to remove the headers ... ?
My personal favourite is the "one pin at a time" as reported here:
Desoldering a 6-pin header with a soldering iron will be a destructive process, as you won't be able to heat all the pins at once. Embrace the destructive nature and desolder it in a way that will protect your PCB. Chop away what you can of the housing with nippers, dremel, dikes, whatever, and then remove one pin at a time with whatever method you choose.