This mod is ridiculously unbalanced compared to the vanilla weapons. A lot of the weapons require major changes to become more in line with the vanilla balance. Here are my suggested changes:

Broadswords:

• Now considered two-handed, meaning shields are incompatible with these types of weapons, for balance reasons.
• Slightly decreased attack speed (1.0 -> 0.9)
• Lower attack damage scaling from 2 to 1 (this means the weapon only gains 1 extra damage per tier, so stone will have 7, damage, iron will have 8, diamond will have 9, and netherite will have 10.)
• Now has an ability, Slash. Works similarly to the sweep on a normal sword, but now deals 50% of the damage of the weapon to enemies hit by the slash.

Daggers:

• New ability: Dual wielding. A dagger can be used in your offhand as a weapon as long as you aren't holding any weapon that is two-handed. (Such as the broadsword)
• Either decreased damage on weapon, or decreased hit range.

Katanas:

• This is the largest offender of the vanilla balance. It's essentially just a more busted version of the normal sword with a pretty decent ability, making it probably the most OP weapon in the mod.
• Now considered two-handed
• Lower damage, preferably lower than the broadsword.
• Slightly increased attack speed (1.7-> 1.9)

Rapiers:
Not sure yet, may update this list in the future with any potential balance changes if needed.

Spears:

• Make attack speed more consistent, at somewhere like 1.2 or 1.3.
• If this isn't already a feature, grant spears extra reach.
• Allow for spears to be thrown, allowing a few enchants like Loyalty to be applied.

Waraxe:
COMPLETE REWORK
Ability changed from Shockwave (now held by the Warhammer, a new type of weapon) to Cleave, an ability that (could potentially have a custom animation, but past that) will swing the axe from above to pierce through 50% of the player/mob's armor. It's drawback is that it can only be used at full charge, meaning you have to charge it a full second.

• Increased attack speed (0.5 -> 0.7-0.8)
• Attack damage is tweaked. (Wood and Gold -> 5, Stone -> 6.5, Iron -> 8, Diamond -> 9.5, Netherite -> 11)

Warhammer (NEW WEAPON):
A redesigned version of the Waraxe with it's ability, and previous stats. It's only change just has to do with the texture. Reason for this is because the shockwave attack thematically fits better with a hammer rather than an axe.

As for a potential new weapon, I have one idea, but I can't guarantee it being great, but here I go:

Scimitar
Attack Damage: Lower than normal sword (Wood and Gold -> 3, Stone -> 3.5, Iron -> 4, Diamond -> 4.5, Netherite -> 5)
Attack Speed: 1.2
Ability: Upon hitting an enemy at full charge, inflict a Bleed effect that will last anywhere from 1 to 3 seconds depending on the material of your weapon. (Wood and Gold -> 1, Stone -> 1.5, Iron -> 2, Diamond -> 2.5, Netherite -> 3) This bleed effect can stack, and only affects enemies with (supposed) blood. (This means it will not be effective against skeletons, slimes, blazes, and other various mobs like this.)

If interested, I could provide sprites for this type of weapon if needed. I've worked for a few mods before like MoreVanillaTools and Total Tinkers in the past, if you'd like a couple examples of my work.

Two-handed weapons could outright disable usage of items in the offhand slot when held. Holding one would hide both the slot and the hand from the player's screen, as well as the offhand item from the third person model. Saying "no offhand item can be used with this weapon that uses two hands" makes more sense to me than "only shields cannot be used with a two-handed weapon," and also answers the question of where the offhand item goes: it stays in the slot, but isn't useable.
This would also prevent the usage of, say, the Totem of Undying with these weapons, for better or worse.