You say audio, but is it a single frequency, or a wide frequency band? 90 degrees correspond to very different delays in time depending on the frequency.
If it is a single frequency (sine wave) that does not change, that can be done with a few discrete components and an opamp. The Picaxe will not be fast enough.
If it is a broadband signal and you want to shift each frequency component by 90 degress, you probably need to do an FFT, then add 90 degrees to each frequency bin's phase, and then do an inverse FFT. No chance whatsoever to do this with a Picaxe or even a PIC16F series chip. At least a dsPIC required.
What is your application? That will help narrowing down suitable choices.
Wolfgang