I would suggest "Don't".
Seriously, if the concern is extraction, it becomes much easier if you're free to select your background color. Shoot with an appropriately contrasting background and extract from the colored background. After extraction, the image can be overlayed on any background including white if that's what's required.
Additionally by selecting an interesting color, you can light it such that hints of that color can show in the clear line for additional contrast and interest. If the goal is to emphasize the colorlessness of the line, use a gray background.
The requirement to have the image on a white background does not mean it has to be shot that way.
--- edit ---
Your comment about shadows suggests that you have the product in contact with the background. You may want to suspend the product with the background far enough away to eliminate shadows.
--- edit 2 Impromptu Shoot ---
I didn't have any fishing line handy but I found some old translucent lawn trimmer line in the garage and some nearly invisible transparent thread from my wife. I bundled both up and hung them dangling in front of some black poster board. I placed a single remote flash on a convenient shelf about 30 degrees behind the target as well as using the on-camera flash for front lighting.
I used a quick and dirty color selection for extraction.
White remote flash as shot
White remote flash extracted with black background
White remote flash extracted with white background
Blue remote flash as shot
Blue remote flash extracted with black background
Blue remote flash extracted with white background
I think a white background is going to be a tough proposition!