Make path-to-string utility as static function

I have a string utility that converts the boost::filesystem::path into a string. The current implementation was done in the following way.

/** header file **/

using convert_typeX = std::codecvt_utf8<wchar_t>;

class Path {

   ...
   ...

private:
   wstring_convert<convert_typeX, wchar_t> converterX;

};


/** implementation file **/

Path::Path(path thePath)
    : rootPath(thePath), searchDone(false)
{
    string filename = converterX.to_bytes(thePath.wstring());
    string rootPath = converterX.to_bytes(this->rootPath.wstring());

    ...
}

This utility is spread across in every class that require path-to-string conversion. After some time when I look back on this code I felt that the design approach is very unpractical and quite troublesome too. Since this utility is used in everywhere, I just wonder, would it be better if I make it static. I'm just trying to simplify things, complex thing is tiring me.

/** header file **/

using convert_typeX = std::codecvt_utf8<wchar_t>;

class FileHelper {

   ...
   ...

public:
   static string convertPathToString(boost::filesystem::path thePath) {
      wstring_convert<convert_typeX, wchar_t> converterX;
      return converterX.to_bytes(thePath.wstring());
   }


private:
   wstring_convert<convert_typeX, wchar_t> converterX;

};


/** implementation file **/

Path::Path(path thePath)
    : rootPath(thePath), searchDone(false)
{
    string filename = FileHelper::convertPathToString(thePath);
    string rootPath = FileHelper::convertPathToString(this->rootPath);

    ...
}

With the new approach, I centralize that piece into FileHelper (a utility class specializes in file). When Path objects need it, just direct call on convertPathToString() from the class.