Welcome to the forum. You would probably have the best luck getting an answer to your question if it were posted to the growing vegetables forum instead of the growing tomatoes forum.
I do grow cucumbers also and must admit I've never tried splinting a broken main stem on a cucumber. I don't think you have much chance of saving it with a splint, but if your going to lose it anyhow, there is no reason not to try.
I grow a lot of cucumbers and always lose a few for different reasons. I seem to feel worse when I lose a valued tomato plant. I wish you good luck with your cucumber plant.
Out of curiosity, are you gardening in Jersey in the Channel Islands or New jersey in the United States?
I simply enjoy gardening!