Any time you have a question about how a spell functions, go ahead and link it so we all are using the same reference.
Okay. Spell description seems pretty clear. Simple action to cast, and the effect is make a small object move. Nothing about requiring a round to accelerate to attack speed seems to be implied to me. The obvious effect would be to use it for hurling rocks, salt shakers, and so on at someone. As well as making the cups and dishes wash themselves or whatever show off things a mage wanted to do. But in this instance, I think we will focus on the attack options. Okay, so 'pick up and attack' seem to me to be part of the same action of the spell.
In the interest of not making this more complicated than it needs to be, but at the same time preserving against the Law of Unintended Consequences....
Using Mage Hand to pick up something and throw it as an attack is accomplishable in one round of activity. You cannot perform any other attacks during this time. Since the duration of the spell is 'Concentration'
you cannot cast any other spells while maintaining a Mage Hand. But in future times, should you be using Mage Hand to hold something up and wanted to perform an attack with a normal weapon, it will require a Concentration Check to maintain your Mage Hand.
Damage for Mage Hand Hurled Objects will be a variable of course, but you will not get your Dexterity Bonus to the Attack Roll. If you took Point Blank Shot, I might allow it. And if you took 'Finesse' I think I would let your Spell Stat Bonus (Cha for Oracles) count into your Attack Roll, but you probably have better things to do with your Feat choices.
For the application in the current situation, dagger or other type of thrown kitchen pointy object will be 1d3. You can hurl more strongly with your arm than you can with the Mage Hand, so damage is reduced. Also, pretty much most "Level Zero" spell effects do 1d3 damage and I see no reason to alter that.