Could "shazam" be used to describe a ninja?

Grammatically, you definitely could use "shazam" as a verb for the action of a ninja appearing. At the same time, to the average native English speaker, it probably will sound "creative," because as you noted, it already has a strong connection to DC comics. "Shazam" is usually considered a DC character's superhero name, and also is that hero's catchphrase. So it's atypical to see the word as a verb in a sentence unrelated to the DC hero, even though it would be grammatical.

It's ultimately context-dependent on your product, how much of an association you are ok with. Having a creative word usage can intrigue your audience, catch their attention, and make them remember a product more. At the same time, sometimes unexpected allusions take the focus off your product and on to something else (the DC character).

A word I more associate with ninjas is "bamf" or "bampf," but I mention this one as one to avoid, because of association to the hero Nightcrawler from the other big comic brand - Marvel.

Some non-comic book related ideas:

The ninja appeared.
The ninja vanished.
Like teleportation, the ninja was there.
Poof! There is the ninja.

Actually, "poof" is really very close to "shazam". Possibly that instead, and then you take out the worry of comic book references?

The OED is helpful. Note the 1964 quotation in which "Shazam" is used in an advert.

shazam, int.

Etymology: Invented word: see quots. 1940, 1976.

Children's slang.

A ‘magic’ word used like ‘abracadabra’ or ‘presto’ to introduce an extraordinary deed or story.

1940 Whiz Comics No. 2 5 ‘Speak my name!’ ‘Shazam!’..As Billy speaks the magic word he becomes Captain Marvel.

1964 Playboy May 63 (advt) Shazam!