I forgot that Zorofans don't read.
Here you can directly see that:
A) Shanks told MH directly that he wasn't in good mood and would be happy to kick his ass
B) Mihawk admiting that he need to settle scores with Shanks (implying that he lost) but giving a pathetic excuse
C) Then giving a picture of Luffy to avoid the thunder.
It's in his genes to ran away from battles.
EDIT: Sorry, now that I think about it you're correct. Shanks never challenged Mihawk. It's the lesser party that must challenge their betters. Considering that it's Mihawk that needs to settle the score between them it's only correct that he does that. But he's too scared to try. My mistake.