I've been playing around with this idea myself, as I have a "witch" character I'm working on , rather than the standard mage/wizard etc. So staves, and wands wouldn't really fit her.
You could always have them use books/tomes as weapons. Could have it floating in front of them in battle, or it could just be something static that they hold and read spells from.
Alternatively, there's always the "guardian"/"familiar" route you could go down, whereas they summon a beast to fight for them.
Or maybe mix it up? Maybe create your own unique class of character. Make a magic user that uses maces, or is a magic archer/swordsman. Have a magic user who only uses dark magic, therefore they wield scythes.
Have a play around
I have scythes as a magic weapon because... well, they're more useful as a symbolic weapon than something you actually swing around. Like they're very impractical if you try to use them as a sword, so I retooled them into magic conducting weapons.
Playing / tarot cards are another neat idea for magic because of sleight of hand and other associated magical properties.
Giving them a shield as a weapon would be another good oddball use like Vexen from Kingdom Hearts - they can use magic and defend at the same time.
Magic tomes are another good staple.
... but generally I would give them whatever is the coolest, like I have one witch that uses gemstone themed spears.
You can also just have them use spells. In some tabletop RPGs, spellcaster classes will have a variety of spells that cost mana/spell slots/whatever resource to cast, but also have a basic attack spell they can use freely. No reason their weapon has to be a physical tool.
There's no need to weasel so much with classic DnD caster's weapons. If you wish to create something unique, then take a look at ezoteric websites about gems, metals and use imagination.
For example, my sorcerer (in my project) as a weapon uses gloves forged from different metals for various spells, and gems are boosters:
Gold - king of all metals, ruled by Sun, attracts wealthiness and luck in all life aspects.
Silver, Platinum - are used for spiritual development, ruled by Moon, increases intuition and helps to see what others can't.
Copper - Ruled by Venus, helps to find love and appreciation from others. Increases aura of wizard who wears copper items.
Iron - Ruled by Mars, dedicated to warriors (but there's nothing in way to combine it with sorcerer) and make brawl magician and Iron would help in winning disputes etc.
Tin - Ruled by Jupiter, metal for dreamers, helps find correct path in foreign lands and increases safety and sympathy.
So in my case, my hero wearing golden gloves have increased healing powers and when he change them to silver gloves my hero can communicate with astral entites and so on.
I don't know what setting you took in your project, but you should check myths and legends related to your settings.
I've seen various fantastical stories utilize uncommon things for magical purposes. Instead of a staff or wand, they would use objects of similar shape, say like a broom or something.
Another option is to have the item be something that is relevant to that character. For example, and artistic character using a feather pen to cast magic or a necromancer having a bone staff. That way it also ties back into the character and story.
Though I find that this works best in modern settings.
Gems. Cards. Books or Scrolls. Miniature animal replicas. Voodoo. Their own hands. Needles. Conjured, Illusionary Weaponry.
Additionally, consider that any ordinary object could be a "spell focus" for a mage, perhaps even different objects for different spells. If you want, check out the Spells section of the Ars Magica rulebook (this 4th edition rulebook is a free, legal download from the IP holder) for a ton of inspiration on items that a mage might use as a spell focus.
I don't know about all y'all, but a good old ritual knife is a thrill for me. Daggers usually aren't even powerful weapons in RPGs anyway! Barring that, I like the idea of weaponized magic scepters... AKA, maces.
Though blunt, modern Wiccans use a special knife called an athame to work some of their magic(k). Other cultures in history and in make-believe have also used knives, daggers and short swords for ceremonial or cultural functions. The Indonesian kris, the Scottish Highland sgain-dubh ("skeen-doo"), the Sikh kirpan (similar to the Yemeni jambiya), and so on. Shucks, even a sword-and-sorcery cultist's versions for fell sacrifices.
Alternatively, if magic isn't exactly divided into arcane / "black" and divine / "white", why not maces and other cudgels? There can be variants that are better for casting (wands, scepters, etc) if desired. Though maces are normally weapons of war, D&D had given cudgels to Clerics for the longest time. Apparently it's based on a vague, medieval Christian tenet (or some muddied version) against spilling blood. Internal damage is more key to blunt weapons than blood-shedding blades.
Hmm...you'd think in this day and age, what with Japanese Schoolgirls frequenting anime, JRGs and whatever else...that someone might have made some gym clothes for the generator. You know, the ones with the short bloomers.