I've also got to side with the 'melting pot' theory...
Before there was extensive evidence of African sailors, there was evidence of the stamp 'n' go callouts and such (at least according to the historic references I've read). I'm not going to knock the contributions of the MANY African nations to the shanty, but I'd also say that a large majority of the traceable influence comes from the 'golden age', long after the art of shanty singing was already established.
One MAJOR way that has been surmised that this influence hit was from some plantation owners sending excess slaves to sea during the winter 'fallow' seasons. They could sell the slave off, thus saving themselves the expense of maintaining slaves during periods when the large numbers needed to plant and reap were not needed... in the process, these slaves would take with them their work songs, which would then very easily spread if not in exact form at least in spirit amongst the other crew.
It's a hard call. I've read some VERY persuasive essays that say that the African trade routes were the genesis of shanteys. I've also read some VERY persuasive essays that say that the Irish 'coffin' ships (starting with the earliest emigrants) were the genesis, that traditional Norwegian whaling songs were, and that many other nations were. Me? Once again, I think it was the real melting pot in action, melding together every influence that caught a sailor's ear into what could stand as one of the only truly international folk art forms.
Gee, that sounds important.