Will the spark snapshot be on this new chain?
No, spark snapshot will be taken at same time from old PTS (last block of PTS at December 14, UTC).
Therefore it is incumbent upon the new PTS team to make sure that the old PTS are not tradable after the December 14 snapshot. I know there are people out there that will try to sell the old PTS after the snapshot to unsuspecting people who have not heard about the new PTS.
This strikes me as highly unethical, even fraudulent, behavior and therefore it is sure to happen.
You should do all you can to prevent it from happening as well as warning all involved.
This is your biggest argument for the exchanges to treat this as a chain upgrade and discontinue the old one at the same time. They won't want to collect fees in trading the old PTS known to be worth zero after the snapshot, so this would be in their best interest.
And you certainly don't need this controversy for your new PTS reputation.