This fully automatic cactus farm works highly efficient, is enormously cheap, simple and completely without redstone to build. As soon as a cactus grows, the block drops due to the neighboring blocks occupied by the shields, falls into the water stream and can be collected through a funnel.
The farm is arbitrarily expandable and can therefore be individually adapted to your cacti or green dye needs!
The size I have pictured is perfectly adequate for my survival world.
Integration of the farm into my survival world (approx. from minute 1:30):
Instructions:The screenshot should be self-explanatory.
The sand block on which the cacti grow must be supported by another block, here I used sandstone steps. For lighting I decided to use Glowstone, to which I attached signs. The shields then cause the growing cacti to drop, allowing them to be harvested highly efficiently and cheaply.
If you still have questions, feel free to ask them, I'll be happy to answer them in comments and then add to this tutorial here accordingly!