Try sketching some arcs/lines on top of the edges. You most likely won't be able to get them to exactly match the edges, but you should be able to get them close. Add your dimensions, and then if needed create a new layer and move the sketched entities to it. Hide the layer and they won't appear on your drawing.
Nick, a lot of the geometry that Solidworks generates isn't dimensionable in a way that's useful for manufacturing or inspection.
Basically, when you make freeform cuts using lofts and surfacing the only way to produce the part and verify its accuracy is to make the CAD database the controling document and require manufacturing have the right CNC and CMM tools to make use of it.
It makes it sound like there was no way to manufacture organic goemetry before the advent of 3D CAD but ofcourse that's not true. what technical drawings used to do is provide ordinate dimensions or tables corresponding to points on the subject
So what you're going to need to do is create sketch points and reference geometry on your model and dimension to those.
For some reason I couldn't select the edges I referred to in order to generate any sort of dimensions.
Now I find that I can generate a sketch by converting the lines on the drawing to sketch lines, then I can add reference dimensions as John suggested. Our manufacturing group has access to our Solidworks models so they can probably generate a CNC program to produce the parts.
Many Thanks, Gentlemen.