Couldn't you do a pack n go to move the files.
My concern with pack and go is that I would ideally like to keep these files in the same main folder. So I don't know that I could do a Pack and Go on part of the contents, or move them from one main folder to a sub folder in the same main folder.
For example I would want to move from:
Network Drive/Client Folder/Project Folder
Network Drive/Client Folder/Project Folder/Obsolete
Besides that some, if not half, of these files should stay in the Project Folder, and only the old or developmental files (which we still want to retain and have access to) would be moved to the Obsolete Folder.
You can specify the Path for each file (in the Pack&Go dialog) individually.
Using Pack & Go you can select to copy all files or just use the check boxes to copy certain files there are ways to sort this to not copy hardware as well.
You can also choose to add a prefix or suffix to the moved files such as (File Name)-Obsolete or copy the entire structure over with a "-Rev A" after all files. It updates the links in the copied files so you don't have to worry to much about it.
If you want to dabble with PDM and you have a SW pro license you can install PDM Workgroup. It's not a great PDM solution but it's included with Solidworks and is better then doing everything by hand. There are some other free PDM software solutions out there as well but the ability to maintain links is spotty and if your an early adopter of the major SW releases then they might break more often.