No, there isn't. Since I think that you can technically turn your killing blow into a knockout blow when you're using melee attacks, it can be argued that that's how you soften the blow so that it doesn't kill your opponent.
An unarmed strike can be any kind of blow that uses your body: punches, kicks, karate chops, knee and elbow strikes, headbutts, tackles, drop kicks, whatever you want.
the only thing to stop you from punching someone/something while holding a dagger, is if the DM makes you roll an intelligence check as part of it, and you nat 1 the intelligence check, therefore forgetting that when you punch, you don't punch with dagger points facing at them, or yourself.
As stated in other comments, an unarmed strike is not limited to punches, so if a DM rules to not let you punch with a dagger or shield, use a kick, headbutt, or elbow instead.
Is there any rule that says you can't punch something while holding a dagger?
No, there isn't. Since I think that you can technically turn your killing blow into a knockout blow when you're using melee attacks, it can be argued that that's how you soften the blow so that it doesn't kill your opponent.
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An unarmed strike can be any kind of blow that uses your body: punches, kicks, karate chops, knee and elbow strikes, headbutts, tackles, drop kicks, whatever you want.
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the only thing to stop you from punching someone/something while holding a dagger, is if the DM makes you roll an intelligence check as part of it, and you nat 1 the intelligence check, therefore forgetting that when you punch, you don't punch with dagger points facing at them, or yourself.
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Other than a DM that enforces logic, no.
As stated in other comments, an unarmed strike is not limited to punches, so if a DM rules to not let you punch with a dagger or shield, use a kick, headbutt, or elbow instead.
This was actually one of the most helpful things you could have said thank you so much