Welcome to the Wicked Edge Forum, “david”.
To actually thin a knife down, behind the edge, like you’re describing is generally attempting to use a more acute angle setting then can be achieved with your WE130. At that low of an angle setting your sharpening stones will probably contact the vise and/or jaws before the stones will impact the knife’s side steel where you need the stones to remove the steel. You may be able to apply a more acute secondary bevel behind your original knife edge bevel, or possibly even convex the edge profile. This would give some improvement in performance but not as well as thinning down the knife sides behind the edge. You may be able to go a degree or three lower then the primary bevel, that is the edge bevel angle, with a secondary bevel, depending on how acute the edge bevel angle is to start.
Using a low angle adapter, or a riser block under the vise, or probably both, will help you to reach a lower angle setting before the stones make contact against the vise and/or jaws. Based on my experiences it takes modifications to the WE130 to be able remove steel from the knife sides behind the edge to thin the knife down like your suggesting you’re wanting to. In my experiences without accessories and/or modifications it hard to set the angle much lower than 15° for a full size chef’s knife with my WE130. It’s easier to set a lower bevel angle on a larger, taller knife then a smaller folding edc knife.
You could attempt it using a Tormek Small Knife Holder. It holds the knife offset by the handle. It would position the knife out away from the vise. But it won’t hold a knife as stable and immobilized as needed for this task.
This would definitely be an easier process with a belt grinder because there are no angle constraints. The knife can be held against the belt any way you need to. You do have to watch you don’t overheat the steel. It’ll remove the tempering and hardness if it gets to hot. Maybe you can find a local knife sharpening service to do that for you. It’s probably worthwhile sending it off to a professional knife sharpener or maybe even replacing the blade from the factory.