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In all the current transformers I have used, there has only been one winding, the "primary" being the active line of the mains cable passed through a hole in the transformer assembly.
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So that's a 1 turn primary and the other winding (secondary). Just because it isn't much to look at doesn't mean it is not there! But is that enough to extract enough energy to operate a relay? I assume that these are normally just for measurement.
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Therefore, the "primary" is the mains lead and not likely to be doing anything weird in the event of a short circuit
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A short circuit is very weird! It means for the time it takes a fuse to melt you have the entire mains across the primary (however small it may be). In that very brief time you have a lot of energy flying about so my proposed device must be safe. Not so hard when a current transformer is just for measurement I guess but in my case it has to be coupling enough to extract significant energy normally.
My problem is that I can see potential problems but do not have a feel of just how bad they are.