A Microsoft file hosting and synchronization service.
Hi there, appreciate this is an old(ish) thread, but wanted to provide one potential workaround for you.
Working on the assumption that you have admin rights on both of your machines, you should be able to drop any shortcuts you don't want to sync in your OneDrive Desktop section in to the Public Desktop (C:\Users\Public\Desktop). Anything put in here will be available on your desktop (albeit it won't show in the Desktop folder in File Explorer) and won't sync to your OneDrive.
You may already have come across this or found a better workaround, but wanted to make the suggestion in case it was of any use!