If you define Natherzim as actual demons, they got arcanists using arcane.
Other Natherzim used different schools as well, like Kin’tessa, that uses nature magic - Mal’Ganis used combined school spells nature/shadow, Balnazzar uses arcane based domination spells, Vagath the Betrayed uses nature, so on and on.
Other Demons using Nature (ignoring things like thunderclap, tar expulsion, accid spray and the like) is Xavius, Imp Mother Folnura, Temptrests, Man’Ari Tauren (Tugar Bloodtotem and co - also uses elmental magic, frost/fire), Bestrix, among many more.
I totally forgot the point (I blame my brain), but you got arcane casters as well, sorry - Belac, Vizuul the Twisted (Man’Ari), and a bunch more I forgot to note. Theme being - benefical or focused damage spells seems to be arcane themed, even if called ‘Fel infused’.
Other demons using Holy Y’Beda (Man’ari), Y’Sorna (Man’ari), and some other Man’ari NPCs sworn to the legion. Very fanatically so as well. Would explain how, as it would basically just be the scarlet crusade reasoning. They truly do believe they are justicars on behalf of the Burning Legion. Side tangent: As they are the only winged Man’Ari Eredar (except Kil’Jaden), are they blessed by Sargeras for their fervor?
Then you got the infernal type demons, Blasphemy, that uses arcane spells, same as wild imps.
Also you got devour magic and spell purge, both being arcane (https://www.wowhead.com/spell=204885/devour-magic). The classic felhound nomnom spell purge and stop - for context. Demonic Tyrant gets hasted by arcane.
Never forget the classic chaos magic, that is treated as all spellschools at once (dated - but reappearing in DF here: (https://www.wowhead.com/spell=418558/chaos-bolt). Mind you, another Natherzim.
And all the “chaos” spells, that is supposed to represent demons unleashing ‘chaos’ magic as inspired from Warcraft 3, like (https://www.wowhead.com/spell=253679/bad-breath).
I gone through over 300 demons, there are still over 2000 to go, that from Legion to DF.
Now, pattern seem to be that Natherzim can use whatever they want (if they even are demons, as per SL lore). Other demons seem themed to use arcane to control or focus their fel based spells - or use it as pure beneficial time/haste based effects. Then, you got things like felhounds - just noming or suppressing/controlling magic and that is arcane. Blink and such, fall into this category.
Hope you find this helpful on your quest to decide if you feel it to be right if Man’ari can use the arcane or not.