Standard Edition of SQL Server and cores
I am thinking we have two choices:
  
  
  Update VM and remove the 3 unused sockets, so we have 4 sockets/8
  cores.
  


This is probably a better option. As Kin suggested in the comment on your question, NUMA imbalance would be a factor by trying to balance CPU affinity across physical cores.


  
  Update VM and remove the 3 unused sockets, update number of
  cores per socket from 2 to 4, so we have 16 processors. I need to
  check if this is even possible.
  


Even if it is, go with fewer cores. On a virtual environment, this is preferred, especially with Standard Edition.

Final note: if you do share the host with other VMs, please be wary of something called CPU lag. This can happen when VMs with different numbers of vCPUs are running on the same host.