"Magical" isn't technically a damage type.
As presented, the weapons still do damage but lose the magical bonus to that damage. If you want RAW support, that depends on whether you are treating the apparition as possessing something like an antimagic field innately.1
As worded, "magical" is a modification (enhancement) to a weapon damage type, typically slashing, piercing, or bludgeoning. You see it listed in an immunity or resistance description in the Monster Manual, most often referred to by its absence: nonmagical weapons (or damage types) don't harm creature X, or mundane weapons (or damage types) are resisted by creature X.
Damage Immunities bludgeoning, piercing, and slashing from nonmagical
attacks not made with silvered weapons
Damage Resistances radiant; bludgeoning, piercing, and slashing from nonmagical attacks
If the magic goes away from the weapon it still does slashing, piercing, or bludgeoning damage. (It's a fair ruling that the +1 or +2 to hit/to damage goes away, since that's magical, in the case that you are making for your custom apparitions).
Is a magical weapon a "spell effect?"
If you treat these apparitions as carrying around, or having an innate, antimagic field(AMF) -- confined to themselves -- you will be consistent with the rules on AMF to rule that the magic on the weapon won't cause the apparition harm. (The +1 or +2 bonus, etc).
Magic Items. The properties and powers of magic items are suppressed
in the sphere. For example, a +1 longsword in the sphere functions as
a non-magical longsword. A magic weapon’s properties and powers are
suppressed if it is used against a target in the sphere or wielded by
an attacker in the sphere. If a magic weapon or a piece of magic
ammunition fully leaves the sphere (for example, if you fire a magic
arrow or throw a magic spear at a target outside the sphere), the
magic of the item ceases to be suppressed as soon as it exits. (AMF (8th level) spell description, SRD V_5.1)
What type of damage is "magical?"
Damage types listed in the PHB:
Damage Types Different attacks, damaging spells, and other harmful effects deal different types of damage. Damage types have no rules of their own, but other rules, such as damage resistance, rely on the types.
Acid. Bludgeoning. Cold. Fire. Force. (Force is pure magical energy focused into a damaging form). Lightning. Necrotic. Piercing. Poison. Psychic. Radiant.
Here's a sticky point. Fire damage is fire damage, regardless of whether you got hit with red dragon's breath, a fire ball, or got pushed into a pool of lava. Likewise with lightning damage.
You can (if you like) make distinctions between magical and mundane.
Since you are the DM, you can choose to make a distinction in your world between magically created (artificial?) damage (other than Force, which is pure magic) and mundane damage if you so choose. That's up to you. If you do this, make sure to advise your players that is how it works in this world. (And you need to keep track of this ...) While I think it is a needless complication (more to keep track of for marginal value) you can do it if you like that sort of thing.
1 While I've always thought that a magical creature possessing an antimagic field or magical resistance to be a paradox, and inherently contradictory, that's a personal opinion not shared by D&D designers. Demons as far back as OD&D Supp 3, Eldritch Wizardry, had varying levels of magic resistance.