@AndrewStacey Is that possible? Is it actually what should be done here? If you apply shorten to the path, it changes the curve irrespective of whether you split it into components, right? So if you apply shorten only to the original path, the components won't be precisely on that path, will they?

% ref: chat.stackexchange.com/transcript/message/65819700#65819700
%\url{tex.stackexchange.com/a/720532/86}
\begin{tikzpicture}[
  fancy dashed/.style={shorten <=5pt,shorten >=5pt},
  ]
  \coordinate (yy) at (6.8,-0.4);
  \coordinate (ww) at (7.75,0.7625);
  \coordinate (pp) at (0.75,-2.25);
  \coordinate (qq) at (2.5,-2.25);
  \coordinate (ctrl) at (9,-1.5);
  \foreach \cdt in {yy,ww,pp,qq,ctrl} {
    \fill[cyan!50!black] (\cdt) circle[radius=5pt];
  }
%   \path[spath/save=pparrowyy,draw, fancy dashed, line width=2mm, -{Butt Cap} ] (pp) to[out=-30,in=230] (yy);

Here the grey line doesn't follow the same path as the black one, regardless of the fact it isn't split. So if the original path is shortened, don't you want the components to adhere to the that path? I don't know how, exactly, but it seems to me that's what would be expected? That is, as a user, I'd expect that the bits would adhere to the original.

Actually, I think I'm missing the point. Is the point that the green is closer to the grey, but it should be closer to the black? Sorry, I probably ought to think about this instead of typing nonsense.

[I changed some of the colours because I couldn't distinguish things very well on my screen.]