A recent (detailed) posting of mine was declared over-rated (-1) and hence my telegraphic attitude. But the nice way you point out that, deserves compliment.

Dear Asok,

up to now, I didn't give you any negative 'Karma' point, neither in this thread, nor in any other!
Don't take this 'Karma' point too seriously. It 'only' expresses the opinion of an individual. And so, a 'Karma' point tends to become a 'Karamba' point, sometimes...

Now, having a look at your schematic, things are much much clearer now:

You can ease the control of LEDs and reduce the flickering, when you use serial shift registers with output latch, so that you can actualize next column, while actual column is still driven by latched output. CD4094, 74HC595 and TPIC6A595 seem to be a good solution, from this point of view.

What current must be sinked by outputs of shift registers?
As always one of seven LEDs must be sinked by each output of shift register, 7 x nominal current must flow through each individual LED. Only by this, whole LED array will shine bright!

As you told, that you must take what market offers, I guess that high efficiency LEDs are not used by yourself (?). So, nominal current through standard LED is about 10...20mA. This means, that each output of shift register must be able to sink about 7 x 10...20mA = 70...140mA!
But this is way too much for a CD4094 or a 74HC595. If you will avoid the use of additional sink transistors, then only TPIC6A595 can be used!

Kai