Critical situation that may result in a close shave (5,4)

I believe the answer is:

razor edge

I'm a little stuck... Click here to teach me more about this clue!

'critical situation' is the definition.
'razor edge' can be an answer for 'situation' (I have seen 'hazardous situation' mean 'razor edge' so perhaps 'situation' could also mean 'razor edge'). I'm unsure of the 'critical' bit.

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for razor edge that I've seen before include "hazardous situation" , "Critically balanced situation" , "Very sharp cutter" .)

I've seen this clue in the Sydney Morning Herald.

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