Your brakes not working in the rain is more likely caused by old dry pads and or dirt encrusted on the pads and rims.
While these brakes will not be smooth as glass without the little plastic thingies you still should be able to make them work. The missing parts should hot a huge effect on the brake not centering or retracting when you let go of the lever. Is the inner cable moving freely?
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“One morning you wake up, the girl is gone, the bikes are gone, all that's left behind is a pair of old tires and a tube of tubular glue, all squeezed out"
Sugar "Kane" Kowalczyk