Balance-Wise This Should Be Fine
There's already an unrestricted 4-armed race in Pathfinder, the Kasathas (a core race in Starfinder), so in terms of balance this would be strictly weaker than their multi-armed racial trait. So if player character Kasathas are considered balanced-to-overtuned to you, then this could serve to reduce their power to be more in-line with other races.
That said, there is some merit that Kasathas as printed are pretty dang strong regardless of the multi-armed trait, with a +2 dodge bonus and +2 Dex/Wis. Even reducing the multi-armed trait to only allow holding items with the extra arms might not bring them in line with other racial options. But that all depends on what you're balancing this option against, or if you even wanted to enable other multiarmed races than this one.
Outside of balance there's also at least one Kasatha option that might be directly impacted by this change in the Bow Nomad Ranger archetype. If you want to allow their ancestral dual-wielded bows as an option, it could be worth making sure this change still enables such characters or noting that they aren't supported.