If he has a huge list of stuff that he wants, maybe make him write it down and you might have to limit how many of each(maybe only one or two garlic extract grenades...I'm not really sure how that works...) When he runs out, have him make declarations (resource or craftsmanship or contacts whatever skill is appropriate...possibly deceit to steal some of the stuff).
Most of this stuff is easy to come by - except the grenades: you can buy holy water at any "mystic" shop (or steal it from any catholic church who usually have font of the stuff as you walk in), iron shurikens can just be on his character sheet...especially if he crafts these things himself. He's a ninja afterall. If he wants a huge list of specialty shurikens like silver and holy etc... I'd might make him aquire them in-game.
Also remember, he's not always going to be carrying this stuff with him.
Here's an example character I have for starting equipment. He's ex-special forces
Weapons:
M4 (weapon 3); Suppressor
Korean War riot gun (weapon 3)
Pistol: MK23 with tactical light(weapon 2)
Knife (weapon 1)
2 grenades (weapon 5/1 zone)
1 Flashbang ("blinded" aspect 4)
Gear:
Night Vision goggles
Kevlar vest (armour 1) concealable
Flak Jacket (armour 2)
Pick-up truck
Apartment
My justification for most of the gear is he stole it before he went AWOL. If he uses those grenades, he'll have a hard time coming by more...same with a lot of the equipment there.
Lastly
If you're stressed about him having too much, then you can just say, "don't worry about equipment...we'll cross that bridge when we get to it"
Then let declarations take care of the rest. When he says, "I pull out my iron shurikens" you say, "sure...don't even bother rolling"
When he says, "I pull out my garlic extract grenade", you make him roll a declaration with a difficulty based on how likely it is that he has one. (or he can just spend a FP and have one). If he's aquiring these ahead of time, in preparation, they'll be easier to get - either because you can lower the difficulty or you can just have him spend the time to get it.
Ninja's are super cool because they spend the time to be prepared. But if they're going in blind, they might not have "just the right tool" so, in that sense, you may want to limit what he has and let declarations take care of things.
It'd help if he had an aspect like "always prepared"