Thanks all for your input.

Kodak Safelights model C is metal, very similar to Model D except model D have 3 wires and grounded.
Here a model D (took on eBay)
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My model C socket is this one
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2 wires, no ground and non polarized plug. You can see also the ON-OFF chain mechanism.
As the cord is pretty stiff I wish to change with new cord, the one I have is polarised plug (at right in the picture).
I supposed that it is not a problem to replace a non polarized by a polarised plug. I will plug it correctly NEUTRAL, wider blade, ribbed wire on the silver screw.
I read online "Most non polarized appliances are double insulated" but no explanation about the double insulated. Is it relied on security feature?

The 2 circuits added in the darkroom is GFCI but adding an outlet on the first appearance in the line. The 3th circuit, the original 2 room outlets are not near the sink and not really used. Rfesk, the problem is not the house circuits but only the safelights that came with non grounded plugs. My question was about if the non grounded is still GFCI protect. Answer look yes.

We can see the same problematic of grounded vs non grounded safelights also in the Kodak model B (round 5 1/2" filter) Newer model is 3 wires grounded and older is 2 wires non grounded. Illustrations from eBay.
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Another safetly question. If I said that I will turn OFF the lamp before touching it, for reoriented it for example. Is it better to unplug it or the Chain pull ON-OFF will cut all current into it.