If he does step down, the Dems will demand that a Democrat be named to replace him. Christie and the Republicans, of course, will go along with it, otherwise, the Democrats might say mean things about them.
Most likely he will go to jail, and keep his job by voting by proxy.
If Christie puts in a Dem he might as well stick a knife in his own back.
There is a zero% chance Christie would appoint a democrat. Zero.
But if he appoints another loser placeholder who won’t run in the special election, that would be pretty much the same thing.
It’s been suggested he’d seek the seat himself if he intends to pass on a WH run.