Ok lets see what we actually know for a fact :
- Shanks and Kaidou had encounter
- Just day after Shanks arrived quickly without any damage / wound being mentioned or visible
- Shanks is on Kaido list of 5 people capable of fighting him.
This list consists of people with greater portrayal and bounties than Kaido like Roger and Whitebeard and Oden guy who already proved his capability to wound and defeat Kaido were it not for old hag assistance.
This proves Kaido did witness Shanks power , otherwise he would never include him into his list.
Now stacking evidence is that we have Egghead and Wano feats of Haki negating devil fruits power regardless is it logia or zoan type . One of them was Shanks himself with Grenbull but another one was Joyboy haki against Gorosei. Yet said haki used against Gorosei got compared to Shanks own haki power.
Conclusion :
As we saw in first image I provided its said Shanks was involved in minor clashes , that it was minor clash against Kaido is also supported by fact Shanks arrived so quickly without any wounds at Marineford.
People may say nothing happened at all , but if that was case Kaido would not have witness Shanks power so he would not list him as someone capable of fighting him, If he didnt saw Shanks power Kaido would never place Shanks in same basket as Whitbeard and Roger.
Given all this facts and feats we had i Egghead its pretty clear Shanks used his Haki to wifi diff Kaido and made him return home without trying to take Whitebeard head.
Shanks > Crydo pretty much everything but confirmed.