Is it possible to do a mass database change to modify one specific custom property but selected files?

If you don't have programming resources, I would second Michael's suggestion to add the variable to the folder text box (temporarily) then run the update command. You may be able to move the files that need to update to another folder just to do this, then move it back when done.

Another option is to create a transition to a workflow. Maybe call it "Variable update". Then write the description variable via a transition action and have it auto transition back to the original state.

Last, while its frown upon doing database edits, the VariableValue table is one of the safer tables to edit but you still need to know what you're doing with SQL, spend time understanding the table format, do this in a test environment....and always backup. However, if the value is mapped to a SolidWorks file property, it will not update the

value in the file, only the DB. The other methods above will update the file.

It would be nice if SolidWorks would give us some better admin tools to do this kind of stuff, edit history, etc. so you don't have to consider hacking the DB.

You can also try a right-click Dispatch action - it would at least allow you to select multiple files in one folder and change the variable - automate part of the work.

I'd be careful with letting Dispatch check stuff back in tho, sometimes it checks out more than you expect. 

Good idea above to use the folder card to update files - where conditions allow.