I legit feel your pain ... Mihawk fandom didn't got a L in this chapter ... they took many W ...
but
Oda took you guys to the edge of ultimate victory but refuse to give it to you by adding few simple words
that's shitty
Yo
Let's see how you answer this dilemma:
The main sources of offense in One Piece are devil fruits, haki, brute strength and swords.
Shanks has no df, doubt he has much strength with one arm. He has haki and his sword.
One of the first skills Mihawk taught Zoro was coating his sword with arm. haki and denied him liquor until he achieves this.
We know Shanks can channel his conq. using his sword, and it's naturally what top tier swordsmen do.
The question is, how can Shanks compete with Mihawk when he has a physical handicap, being outskilled and an inferior sword?
The very least he can do is use his special haki and fire sword to narrow the gap, which is apparently not enough.