Hello.
This is a very interesting case.
I am going to assume certain things:
The old Storage is an EMC VNX Storage, the new storage is a DELL EMC Unify Storage, both are connected in a SAN (Fiber Channel) with the ESXi Hosts.
There is a vcenter Server that manages ESXi hosts with versions 5.5 and 6.0.
Depending on the type of licenses you have, you could perform a storage vmotion of the VMs from the old Storage to the new one. You should check with your EMC vendor if you have an internal tool in your Storage to migrate the boot luns of each of the ESXi Hosts. You must define the ESXi hosts with their HBAs on the new Storage. If this is achieved, each HBA of each Host will have to be configured to boot from its own boot lun in the new Stroage. These jobs are going to require some offline time.
Another option: If your ESXi Server has an internal USB port this can be used to install the ESXi on a 2GB, 4GB or 8GB USB key, on each server. Of course, each ESXi Host would have to be configured again. In this option we avoid all the jobs of the Storages and their Boot from SAN.
These are just some ideas that can be combined with others