I do not think you would have to shut down the whole cluster.
For me the order should be something like:
Physical switch: change to MTU on the iSCSI VLAN to 9000. This should not affect anything.
Virtual switch: change the MTU on the vSwitches connecting to the Vmkernels for iSCSI. Should also not disturb anything.
iSCSI SAN: Next change here. However, I do not know if the specific Lefthand SAN has to do anything for this change to apply. This you must check with HP. Perhaps the interface has to be shut down and up or something. This is SAN specific.
All this steps will not affect the actual MTU used. It is a common misunderstanding that all devices must have the same MTU settings or not the network will blindly sent large frames all over the place. The actual MTU being used is negotiated between the end nodes at the TCP session setup. This means that as long as the VMkernel iSCSI is not changed no frames will be larger than default.
So for the final step you should change the Vmkernel iSCSI adapters to 9000, and now all end-to-end devices must be configured with the higher MTU size. For the larger MTU to start apply a new TCP session to the iSCSI SAN must be setup and I does not know any real good way to easy verify this. If possible, it could be good to set a host to Maintance mode, migrate the VMs, change the Vmkernel MTU and then reboot.