I'm no master on the subject, but a Hybrid build is definitely not gonna be easy to gear for effectively especially when you need to start really hitting high DPS numbers (like 180+). We do have some nice damage-type-neutral gears (like Screaming Ghost Party and Overdrive Rampage), but there's not a huge amount of mixable gear that will also boost your skill DPS properly. But since I've made both a Physical and Magical ninja > kagerou/oboro > shinkiro/shiranui, I can note a couple things:
First, I would use this updated Skill Tree Builder because I know the irowiki one sometimes has outdated skill data:
You said no Fire, which is a shame since Blazing Shield/Exploding Dragon make the earlier levels go super easily, but I would then focus on Snow Flake Draft as your leveling AOE I suppose... It's a great skill but until you unlock 16th Night as next job, it will not be a ton of fun due to cast times. Maybe using Ninja throwing skills but I think those got nerfed long ago?
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Second, the irowiki calc limits the ninja class to Base 160 but you can get to Base 200 for stats (200-250 uses Talents, so not applicable on that calc), so switch to any main job, like Rune Knight, so you can build your stats up to 200. How you hybrid is also going to affect stat spread, but:
- For PHYSICAL: I'd recommend Kunai Splash for earlier levels and Swirling Petal for later (depending on gear budget) until at least 200. Both are boosted by STR rather than DEX primarily, but AGI affects Swirling Petal damage (if not getting Petal, can lower AGI for more DEX/LUK). I think Kunai Explosion got some gear that boosts it now, but I don't know if it's worth getting.
- For MAGICAL: Snow Flake Draft + Ice Charm + 16th Night will be your bread and butter until 200. You can just use Wind skills for water-type enemies.
Something like this might work nicely:

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Good luck with gearing up in the later levels, but hope this advice helps a little!