Small cories would stuggle eating them. I see some adult cories that eat a slice of cucumber. They work from the middle and outwards. Pet stores just leave the cucumber for a couple of days. I wonder if it contributes a lot of ammonia though ... hmm.
There's so little nutrition in cucumber it's hardly worth the trouble of feeding it. It does need to be weighted down. All my catfish (and snails!) love tomato; you could try that, or lightly cooked courgette, or peas as the other posters have mentioned.
They shall eat cucumber since they are natural scavengers, Blanch the cucumber in hot water for about 30-60 secs. That way it will sink and the natural liquids wont cloud the water.