Basically, I want to have my sketch have a solid color in the inside the path (with live paint), but the path itself that has a stroke, which looks like a border on the image, I want to be completely transparent, so when put on a background you can still see where the border would be, but the background will make it up.
You might have to make 2 objects, one with just stroke, and one with just fill.
I was going to suggest making your stroke either black, white or 50% grey, then set it as screen, multiply or overlay respectively to make it invisible over another layer. This will make your solid colors affected by the background however, which is why you may need the stroke & fill to be independent.
The simple truth is for vectors you create a gap, and not make a stroke "transparent". In some cases you can simply set the stroke color to match a background color and that is sufficient. A white stroke on a white background appears like it's a gap when it's really not.
If you need a gap, then the most likely easy method to create one is to select the shape with the stroke and choose
Object > Expand. Then select everything and using the Shape Builder Tool, Option/Alt-click the area where the stroke is to remove that shape and create the gap.
It is difficult to provide any further guidance without seeing the actual artwork in question.
Im new to this forum and came upon this question (I was doing some work that needed this effect and this is what worked for me). ((((Duplicate your layers just in case you may need them later before you start!!!)))). Take your vector work and make it 2 colors, so long as the fill is any other color but white, but the stroke however MUST be white for this to work. Select object->Rasterize and rasterize your vector work (there will be a white box around the image but don't worry it'll be gone later. Then select the rasterized object and go to View-> Image Trace. In the image trace menu select MODE to either color or black and white, then check the box "ignore white" and check the preview button. The white strokes should be gone and the colored areas should still be there. Then go to Object->expand. press ok when the fill/stroke menu pops up and voila! Hope this helps.