I understand there is no vCenter with free version of ESXi hypervisor, so no update manager.
Hence the only way to patch is command line.
BTW could you share the link for download of free ESXi Hypervisor.
You are right. There is no another way how to install udpates rather then UM / esxcli. UM is part of VC so esxcli is the only option.
BTW free ESXi can be obtained here: Free VMware vSphere Hypervisor, Free Virtualization (ESXi) | VMware United Kingdom