Burning his BCH would obviously help BCash, as pointed out by others.
At the same time, showing the world that his BTC are a possible part of the circulating supply would harm BTC, also as pointed out before.
If anything, it'd be a statement
pro BCH.
Simply moving his BCH, or signing a message with a few private keys would be a completely different matter.
On the one hand, he'd probably severely harm the BCH market, since liquidity is much more of an issue "over there" than with BTC.
On the other hand, BTC would also suffer from the looming Sword of Damocles.
All in all, it'd probably be a lethal blow to BCH and a serious crash for BTC.
All that without spending a single coin.
![Cool](https://bitcointalk.org/Smileys/default/cool.gif)
Actually selling the coins on the market is out of the question, that would just be calling the SWAT teams to his house.
There's simply no obvious solution how and where he could sell a million BTC/BCH for Dollars or Euros without being tracked down.
Selling for Altcoins wouldn't work, either. Any Altcoin's price would skyrocket as long as he's buying and plummet to (near) worthless once he's finished.
Best case scenario:
Burn the BTC, move the BCH.