I have been having good luck without the capacitors, only because my current-limiting resistors are relatively big, like 300ohm. In case you need brighter LEDs with more currents, use a chip that is rated for that kind of work. the 595 is more or less for signals but not for powering high-current loads. I vaguely remember 20mA as maximal per channel. BTW, 0.1uF caps are very cheap. Got a bag of 0.1uF 50V caps from dipmicro.com for around $10. That's what I did with 0.1uF and 22pF caps
Also, make sure you have enough delay between shifting data and toggling storage register, according to spec sheet, since you have 9 of them. If you don't consider this aspect, your last few lights will not work regardless what you want them to do, since your toggle arrives before the data.