Can I place 9 damage counters on Walking Wake using its "Undulating Slice" attack if it would result in enough damage to knock itself out?
Yes, you can put up to 9 damage counters on Walking Wake even if it doesn't have that much HP remaining. Undulating Slice will do 20x each damage counter that was placed, and at the end of the attack Walking Wake will be knocked out.
Source: Twilight Masquerade FAQ; TPCi Rules Team (2024-05-23)