He didn't wait. That's just how long it took him to reach the place by himself. Lol, what? Do you think fighting Yonko would be a walk in the park or something? Obviously, both parties would be fucked up. An admiral wouldn't expect small-time pirates to have access to world-class doctors. Chopper is literally a pet according to the outside world. He literally just had an easier time dealing with King and others, so of course, he'd expect things to go smoothly with the alliance too unless you're suggesting GB thinks he's stronger than Kaido and Big Mom, which clearly isn't the case given how he's smart enough retreat from Shanks.
The problem is him running away just by sending Shanks its like he wasn't evem Challanging him to fight. If then he would habr run it was understandable but running just because you sensed someone km away and not even damaging a single alliance? Whem every mf were below yc2 except Yamato and the minks were non were non sulong.
It just makes him pathetic talk it all.