Moon-Circuit Hacker

The ninjutsu ability can be activated during the declare blockers step, combat damage step, or end of combat step. In most cases (see below), if you wait until the combatdamage step or end of combat step, it will be after combat damage has been dealt, so the Ninja won't deal combat damage.

If a creature in combat has first strike or double strike, you can activate the ninjutsu ability during the first-strike combat damage step. The Ninja will deal combat damage during the regular combat damage step, even if it has first strike.

Although the Ninja is attacking, it was never declared as an attacking creature (for purposes of abilities that trigger whenever a creature attacks, for example).