Frankly the most dangerous weapons 20th century solders would have are not guns.
I'd say the best/most dangerous weapons are radios and communications. Modern infantry units would have UAVs (and short of massed fire, its unlikely civil war era troops could take them out. )
Even a 'weak' radio with say a 4km range would let you get an hour or so's warning out at 'modern' marching rates.
Even with weapons of the era, knowing where the enemy is, and knowing how effective your fire is would be invaluble. One soldier reporting an enemy column is moving a certain way means a whole load of his side, either with contemporary or modern weapons know where, when and how to ambush them, and know how many of the enemy they have.
This would be a massive force multiplier
I'd use 'modern' troops as raiders - hitting soft targets and resupply wagons. Shoot horses, kill guards and either take or destroy the enemy's supply lines, or to decapitate enemy generals
I'd also consider the impact of other modern equipment, body armour is likely to easily stop lead balls, modern helmets...
And Night vision - since your troops can see the enemy in the dead of the night, and attack enemy forces unseen. Being able to sneak into an enemy base, and tamper with supplies or slit random guard's throats is likely to have an outsized reaction compared to the more energetic ways of breaking things and killing people.