It says "its normal damage type" not normal damage.
Ok put "type" after every line in my post above.
The
normal damage type for a Dragontooth Dagger is Piercing and acid.
Damage type is what the weapon's default damage is like bludgeoning or piercing this has a definition. Some magic weapons or other stuff change a weapon's damage type. A Dragontooth Dagger does not change the weapon's damage type it just makes the weapon deal bonus acid damage on a hit, and so would not be affected by something that changed the type.
The default damage for a Dragontooth Dagger is 1d4 piercing + 1d6 acid.
There is a distinction in the rules between conjuring a pact weapon and creating a bond with a magic weapon. When you do the latter you are not conjuring a "default" non-magic weapon, you are bonding with a specific magic weapon and the damage done by that specific magic weapon is the default damage for that specific magic weapon.
Bonding with a Dragontooth Dagger is fundamentally different in the rules then conjuring a dagger.
Moreover, if this is the tact you are taking what is the "normal damage type" of a Sunblade or a Staff of the Adder?
Finally, what do you do about the magic bonus? If you are only focused on the "default damage type" of the base non-magic weapon template itself specifically, then magic damage is added, just like other dice are added. A Dagger +1 deals 1d4 "default dagger" damage, the extra 1 is bonus damage from the magic. So if I use pact of the blade to bond with a +1 dagger with my 20 charisma Warlock and change damage to psychic, that would mean I do 1d4 psychic + 6 piercing? That makes no sense, but it is what is required to accept your interpretation.
If I can't change the 1d6 bonus acid damage on my Dragontooth Dagger, why can I change the 1 magic bonus on my +1 Dagger?