This would actually work, i think.
Of course, there's the usual DS minmaxing suggestions (change the race to ork, drop LOG, raise CON and Edge), i guess you know the drill to make your character more effective by making him look like any character that underwent advice here.

Also, as usual, unless you have a lot of karma at hand, the character will be more efficient either as a pure adept or pure magician.
So far for the general stuff.
Of course, feel free to ignore it as long as it doesn't fit your concept or otherwise doesn't sound fun to play.
Now for the details :
Keep in mind that for ninja acrobatics, as well as all ninja modes of attack, you need STR.
You could easily boost that with the Improved Attribute spell and a spell lock as long as your natural STR is relatively low, however.
As far as the mystic stuff is concerned, you actually
could represent chi attacks by adept powers.
Killing Hands, Critical, Elemental, Nerve and Penetrating Strike are just that.
There's even an adept power that lets you delay damage so that the victim dies of a heart attack a day later.
As far as i recall, though, all of these powers are in Street Magic and this build seems to be basic rules only.
You might want to pick that book up, it's certainly worth it.
Theoretically, Critical Strike enables you to do devastating damage in hand-to-hand combat even if you have a STR of 1, given a high enough Magic attribute.
If you want to go mystic adept just for the reason of cool hand-to-hand attacks that seem to defy laws of physics,, you might be better off with a pure adept.
BTW, what's the character's magic tradition?
He seems to be Logic-based.
The only genuinly Japanese tradition statted out in SR4 is Shinto Magic (also in Street Magic), which is Charisma-based, though i see no problems with a rational tradition without overly religious components for this character.
You might want to take a look at Wuxia for that and simply change the fluff from Chinese to Japanese, i think that would work out perfectly.
Another approach towards mystifying a ninja concept would be a spirit ninja.
This character would use spirits (most likely kami, but same diff) to boost his ninjatic skills (oh my god, did i just write ninjatic? Yes, i did...).
For example, Concealment instead of Stealth and Invisibility.
For non-combat purposes, that's way better to hide yourself.
Spirits of man could, combined with a decent spell selection, also do amazing things to boost attributes, initiative and various other stats.
I'm not even beginning to ponder the possibilities of a posession-based ninja.
Of course, one would have to design a new tradition for that...with Guardian and Task spirits, it would be easily possible to create an 80s television action series or high school anime ninja who is a normal schoolkid imbued with awesome ninja powers by the spirits of his ancestors (or whatever).
My, one could even take this further by turning the character into a friggin' drake.
I have to stop this line of thought before i get a cheesegasm.
Either way, SR is certainly a system allowing for convincing ninjas of any variety both from history and pop culture and however you finally implement the concept, as a full adept, magician, mystic adept or even a mundane biosam, i think it's on the right way.