I have a small graph drawn in Tikz with two paths through it highlighted in different colours. However, these paths are going to share an arrow. What I would like is to highlight this arrow with both colours, one above and one below so that it the reader can distinguish between these two paths. Is there a way to do this within Tikz? Below is my Tikz code for generating the picture:

```
\begin{tikzpicture}
\tikzset{edge/.style = {->,very thick}}
\tikzset{p1/.style={preaction={%But before that
draw,yellow,-,% Draw yellow without any arrow head
double=yellow,
double distance=.4\pgflinewidth,
}}}
\tikzset{p2/.style={preaction={%But before that
draw,green,-,% Draw green without any arrow head
double=green,
double distance=.4\pgflinewidth,
}}}
\tikz {
%%First graph
\draw[edge,densely dashed](0,0) node[label={[xshift=-.2cm,yshift=-.4cm]$w$}]{} -- (1,0) ;
\draw[edge,red,p1] (1,0) -- (2.45,.5) ;
\draw[edge,densely dashed,p1] (2.5,.5) node[label={[xshift=0cm,yshift=-.2cm]$w'$}]{} .. controls (3.25,1) .. (4.95,0.15);
\draw[edge,blue,p2] (1,0) -- (2.45,-.5);
\draw[edge,blue,densely dashed] (2.5,.5) -- (3.35,.10);
\draw[edge,red,densely dashed] (2.5,-.5) -- (3.35,-.10);
\draw[edge,densely dashed] (3.8,0) node[label={[xshift=-.2cm,yshift=-.4cm]$w'''$}]{}-- (5,0) node[label={[xshift=.2cm,yshift=-.4cm]$W$}]{};
\draw[edge,densely dashed,p2] (2.45,-.5) node[label={[xshift=0cm,yshift=-.8cm]$w''$}]{} .. controls (3.25,-1) .. (4.95,-0.15);
}
\end{tikzpicture}

```

I have just learned how to do this kind of thing in Tikz so apologies for what I'm sure is very bad coding style. 

I'm wanting the result to look similar to [question "Two coloured arrow"](https://tex.stackexchange.com/questions/115205/two-coloured-arrow) but with the black dashed arrow still being visible (and in Tikz if at all possible). Thank you so much for any help you can give!

Edit: Here is a picture of what I'm getting at to make it clearer. Thanks again.
![Double Coloured Arrow](https://i.stack.imgur.com/lFR9I.jpg)