What is the correct usage of 犯險?
http://www.cantonese.sheik.co.uk/dictionary/characters/2546/
  
  犯
  
  [1] [v] offend; violate; go against
  
  [2] [v] invade; attack; encroach on


「犯險」go against danger

「犯天威」go against  the wrath of Heaven (emperor)

「冒險犯難」take risk and go against disaster

It is not in that dictionary, but I would suggest "go and face" is also a good interpretation of 「犯」in this sense.

The main point is: "to 「犯」something formidable"  is to actively go against it, facing it, so your interpretation of " to brave" is quite direct and accurate.


  I have assumed 「犯險 to be 「冒險。But none of my dictionaries contain it. When is 犯險 used? Does it differ from 冒險？


*「冒險」 and 「犯險」 are basically the same, differ only in degree of activeness. You can move forward to 「冒險」,  or you can 「冒險」 by not taking action; but you have to move forward to 「犯險」.

*「以身犯險/以身冒險」(personally go against danger/personally taking risk)is a common four characters phrase, it mentions 以身 (with one's own body) to emphasize the  seriousness of the stake. 


  http://www.cantonese.sheik.co.uk/dictionary/characters/1428/
  
  冒
  
  [2] risk; brave; jeopardize