I have grown cucumbers in containers before. They do ok, the containers need to be watered daily. I use a tomato cage for a trellis.
I don't plant so much in decorative containers, I prefer to plant vegetables in 5 gallon or bigger containers. I find the 18 gallon containers to be the best for most plants. It contains enough root volume for most plants, and does not dry out as fast. I have grown cucumbers in 3 gallon pots but they are better in 5 gallons. I only plant one cucumber in a 3 gallon pot, but I can get a couple on the same trellis in a 5 gallon pot.
Happy gardening in Hawaii. Gardens are where people grow.