How to remove orphan Files and Registry entries?

My situation is similar to that of https://www.experts-exchange.com/questions/20915648/unistalling-different-softwares-on-windows2000.html.  Except more difficult.

My crummy application has no uninstaller at all.  I need something that will trace out the dependencies of reg entries and files and dlls and clean / remove them all!  Shortcuts too would be nice.

My process would be perhaps:  Start with the Desktop shortcut.  Delete the exe to which it points. Run the dependency-chasing program.  Delete stuff.   Perhaps a folder or a dozen files remain that I know by human experience are related to crummy app.  Delete one of those exes or dlls.  Repeat dependeny-chaser; maybe it will find a whole additional set of reg entries and dlls.  Repeat until no further low-hanging fruit.

I have looked at "Registry Cleaner" and "MyUninstaller"  Neither appear to work with with a starting point as messed up and ill defined as what this crummy app did to my 8 workstations.

Thanks, and have a good Holiday weekend
David