I'm in a zombie apocalypse who do I choose to be by my side?... Sesshomaru!
He's a very skilled fighter and someone very challenging to beat. He could wipe out the majority of them if not all with a single strike of his tenseiga. Not to mention that he can transform into his actual form, which is a giant dog, and kill them off that way.
Another helpful feature he has is his attitude. He's a cold and ruthless demon by nature and has killed without giving it a second thought before so killing zombies won't affect him at all unlike others who would get emotional.
I'm confident that he would get out us out of that zombie apocalypse alive and with time to spare.