Everyone is infected so getting blood in or on you makes no difference.
I would say the Walkers have something in their saliva, some other form of bacteria that accelerates death. But it doesn't affect you becoming one.
Jim, Shane, Tyrese all had accelerated deaths but Hershel could be saved. The concern was over if he'd die from the amputation.
Remember the weird strain at the prison that killed everyone and also affected Walkers. There are a few different biological things in this world so I don't think chalking it up to one we haven't had explained yet is that crazy.
The Prison flu didn't affect the walkers. Those walkers were humans that were killed by the flu. The flu didn't impact the walkers at all. You could just identify which people turned because they had the bloody eye flu.