Q:

Plot region in between two discrete functions

I am trying to plot the region in between two curves that I only have as discrete data, without plotting the curves corresponding to the data.
In principle, I could interpolate the functions and then do a RegionPlot with the interpolated functions, but this seems complicated.
The following simple code snippet gets very close to doing the job, so I was wondering if there a simple modification that would get me there.
ListLinePlot[Transpose[Table[{Sin[x], Cos[x]}, {x, 0, 5, .1}]], 
Filling -> {1 -> {2}}, PlotStyle -> Thickness[0]]

Result:

A:

One simple way this can be achieved is by the following options:
PlotStyle -> None, FillingStyle -> LightBlue

The first option turns off the lines, the second allows one to specify the filling colour.
Result: 

