In Inkscape we can break apart the path at a desired location.
- Ungroup all paths from the source SVG
- Select nodes from where we wish to break the path
- Tick Break Path at selected nodes
- Choose Path > Break apart Shift+Ctrl+K
- Select the now generated new object to then change it's color (or delete it, move it, etc.)
In case there are no pre-existing nodes at the location we need to break we can always manually add new ones.