M. N. Dutt's English translation of Vyāsa Smṛti a.k.a Vyāsa Saṃhitā can be found on Archive.org:
Like all other Smritis, the Parashara Smriti also is of the opinion that some human beings and some other beings are impure to touch.
Take a look at the following verse from the 6th chapter for example:
On seeing a Chandala, let him look at the sun without a moment's delay. For touching a Chandala, let him bathe with his clothing on.
Some more references ...
Parashara Smriti is missing the Achara Kanda, that any Smriti must have. So, it does not say anything regarding the details of how the Upanayana ceremony should be performed. But it does talk about the sacred thread which is invested during the Upanayana ceremony.
If, while performing the rite of Achamana, he has his Lead or throat wrapped with cloth, or ...