Replacements for a 4006 IC?
Don't listen to these RadioShack guys, giving such advise is a shame to the shop!
The alternative devices you mention are entirely different. The 4000-series are digital devices and 4006 specifically is a digital shift register, both LM's are analog devices called comparator and opamp repectively. These 4006 chips are pretty standard and shouldn't be too hard to find in a decent electronics shop.
Replacement part:
As Jippie says - the IC is completely different from what RadioShack said. I can understand advice from such shops being 'less than good' on occasion but in this case they are utterly and completely wrong - there is no comparison whatsoever in the functions of the ICs suggested as replacements.
This is an unusual IC and finding an alternative is unlikely. I have not looked to see what else is available but it may be unique.
If essential the same functionality could be achieved with other shift register ICs.
eg 74HC4094 8 stage. This has the advantage of having all outputs available (unlike the 4006) but in one block (4006 has 4 blocks) so 2 or 3 of these would do what is needed with some redesign. They are also much more widely available and also cheaper (about 60 cents in 1's at Digikey).
Availability
The CD4006 is now quite rare.
Here is the Findchips listing for CD4006. They show Arrow, Avenet, Quest all showing stock and 1 off pricing and Nasco with stock but no price shown.
If you are in the US you can find it at Quest in California who may sell in 1's, They have several prices - the cheaper one looks OK.
Avnet also show stock and 1 off pricing
Arrow. 3 in stock?
Circuit
You are probably aware that this uses a PC parallel port to connect to a PC. These are 'rather rare' on new PCs. A USB to parallel port interface may or may not work.
Aspects of the circuit appear marginal - if it works it works - it may be worth looking for other user comments on it.
All diodes except the 3 right most ones pick up +5V from the port and feed it to the Nintendo as 5V supply.
N64 data on pin 2 (not touching ground despite appearances) is taken via R3 to 4006 left pin 1 = shift register input. R3 C1 form a data filter. I am not familiar wit te C64 interface but it seems that clock pulses are also fed via C64-pin 2 using DB25-3 via R1 as clock source. The shift registers in the 2 CD4006's are connected in a long chain exiting at 4006-right pin 9. The way of driving the BC559 is 'marginal" but if it works it works. Placing a 10k resistor from 4006-righht pin 9 to T1-base may make the 4006 happier. DB25-10 is the data output to the PC. It has no pullup and is relying on the port pin floating high when not driven. A 1k to 10k resistor from DB25-10 to say R4 left hand end or some other DB25 pin which is always driven to +5 V may help. But, it may work OK as is.
There is a Russian clone for it К176ИР10 (K176IR10). Still lot of them here in Russia and ebay also sells them: ebay