MarkT:
You have proper decoupling on all these 595's and a powerful enough power supply? There shouldn't be problems daisy-chaining them upto 10 or so (so long as all wiring is short). For 25 LEDs you only need 4 shift registers.
wires will be long, one led at one meter. 595 will be at every 8 led + transistor for driving led. All this will be in transparent tube and immerse in swimming pool.
Is there another way to control this 25 led's, maybe with even less wires from tube to controller with arduino