All possible scenarios considered here, they would likely cancel each other out. Kakashi can maximize the impact of his techniques at the cost of minimal chakra. Raikiri is an enhanced and concentrated version of Chidori, meaning that it's not just a nickname. This means that it would likely be of equal or close to equal power as Sasuke's Yin Chidori.
Yin Chidori vs Raikiri - Results would either be they negate each other, both Sasuke and Kakashi take minimal damage, or Yin Chidori slightly overpowers Raikiri and Kakashi takes minimal damage.
Chidori vs Raikiri - Raikiri overpowers the Chidori due to Raikiri being a more concentrated and enhanced version. Sasuke takes minimal to moderate damage.
I like your idea but that isn't how a clash works. Unless the jutsus completely cancel out or the winner doesn't intend to kill, the winner is not only going to push the force of your jutsu upon you, but he or she will commence their own jutsu
With chidori there are five factors
Speed of thrust
Strength of chakra (all jutsu)
Amount of Chakra (to keep chidori running)
Chakra control: the more compact the chidori the more electricity to fuel the attack.
Excellence/ Affinity in the jutsu
This goes as following
Speed: Sasuke
Chakra Strength: Sasuke
Amount of Chakra: (for a clash it's a tie)
Chakra control: I'd imagine Kalashi
Both are lightning affinity with Sasuke having an edge of mastery over the nature itself