Pink noise is not going to sound like voices; it sounds a lot more like water splashing in a fountain. The high frequencies are small, and it will not just sound like a garbled version of your voice. The reason is that the amplitude distribution you find in your voice cannot be maintained--voice doesn't have a 1/f distribution.
You can maintain the phase relationships from your own voice, but you won't be able to tell the difference, most likely, due to the completely altered frequency amplitude profile. (Ears are sensitive to frequency and not very sensitive to relative phase.)
You can generate it like this (among other things): generate white noise, take the FFT, multiply the amplitude components by 1/f, replace the phase with the phases from your voice, and then invert the FFT. This will maintain approximately the right frequency-to-frequency variability for a clip of that length.
Now, you could also try to pinkify your voice. It wouldn't be pink noise, but rather 1/f voice. You'd need to have a broad envelope over your voice FFT that you could then multiply to get something that went like 1/f. You'd generally need to boost the low frequencies, damp the medium ones, and possibly boost the high ones again. It will sound like a growling mess with a faint voice in the middle of it, if you're lucky. (I'd generally use a spectrogram for this sort of thing; a FFT isn't good enough at maintaining temporal correlations.)