how would a shift register help with that?
A shift register allows you to use a small number of pins on your processor (1 to 3) to control an arbitrary number (essentially unlimited) of output pins.
The device suggested (I assume the same as a 74HC595) is a shift register with a latch.
You send out (in your case) 64 states, one at a time and they filter through all the chips. Then when you have them set up, you activate the latch and all the outputs change to your newly loaded values.
This allows each output to drive a single LED (or more complex stuff if you require)
Because they're not multiplexed, the driving is simple, just a resistor.
As an aside, the specs of some LEDs will include a graph showing you maximum current on one axis, and pulse duration on the other. This allows you to determine the maximum current which can be used safely during multiplexing. I've seen it as high as 1A per LED for short duration pulses. However, the problem is, if your code ever locks up and fails to keep multiplexing the display, the LEDs that are stuck on will burn out *very* rapidly.
Generally speaking, it is the temperature of the die which is a major factor in the aging of the LED. Within reasonable limits, maintaining the same dissipation by increasing the current and reducing the time is OK. There are a couple of caveats though. Firstly, the colour can change when the LED is operated at higher current (this is typically true of LEDs which use phosphors to create a particular colour. Secondly, the light output may increase at a rate slightly lower than the increasing current. Thirdly, the forward voltage increases with current. Two and three provide a theoretical upper limit to the multiplexing because it eventually becomes impossible to achieve the desired brightness without exceeding the dissipation limits (At this point you may also be at or beyond the absolute maximum current for pulsed usage of the LED).
The question becomes... How far can you push it?
For High power LEDs, the limits are easily reached. CREE provides
this advice. It boils down to -- You can double the current for 50% duty cycle at 1kHz, but the limit for triple the current is a 10% duty cycle. They provide a lot of interesting information about current crowding and migration of the metals used in the bonding connections for the device.
For lower power LEDs, you can go further.
Here is a recommendation as to how to handle a particular type of 20mA LED. Notice that the upper limit allows 100mA peak current. Also notable is the observation that the LEDs degrade much faster, but are effectively on for less time, so the degradation over 100,000 hours is roughly equivalent.
The other question you have to ask is "Do I need my device to last 100,000 operating hours?" If the answer is Yes (say for a digital clock) then you need to keep strictly within the limits. If you answer is No (Say for an emergency beacon that may only have a required life of 100 hours) then you can push things a little harder.
With the increasing efficiencies of LEDs, it is rarely a requirement to push LEDs as far as it may have been in the past. One exception is in remote controls, but the chance that you will have your finger on a button for 100,000 hours is pretty small