The 9V will damage the shift registers, and perhaps the Uno too. The high voltage may be causing your ghosting problem also. You should use tpic6b595 (or tpic6c595). These have a higher voltage rating and open-collector outputs.
You should daisy-chain them. Then only 3 Arduino pins will be needed. I don't understand your concerns about daisy-chaining. Your point about delay makes no sense to me, I think you must have a misconception about how they work. The time taken to update 100 shift registers would be too small to measure except with specialist equipment. There would be no delay between the first and last registers in the chain updating because they all update their outputs at the same time, when the latch signal tells them to.
Using led drivers would save the need for series resistors for each led/segment. Some also allow brightness control through your code.