Hi Kralijir,
I understand your concern for not shutting down the VMs, as that would require downtime.
My suggestion would be see if you have enough resources to migrate all the VMs on the ESXi host to other hosts within the infrastructure. If yes, then you will have to migrate those VM's first.
Then put the host in maintenance mode and shutdown.
You can do use to method to update all the ESXi servers one by one.
Hope this helps.
Cheers,
Adil Arif