Sketchy lines applies to an entire view, there is no way to only apply it to certain elements nor lines in a view.
As a workaround, you can overlay two views to essentially have this effect. First, create a new Phase Filter which only shows Existing elements (or use the filter "Previous Phase" and modify it to your liking), and then another which only shows New elements (or use the filter "Show New" and modify it to your liking).
Create two identical views using Duplicate View. Then apply the Existing-Only filter to one view and the New-Only filter to the other. Apply Sketchy Lines to the Existing-Only view. Place both views on a sheet in the exact same position, the New-Only view over the Existing-Only view (I suggest using a Guide Grid on the sheet, then aligning Grid lines/Levels placed in the views to the Guide Grid to align the views perfectly).
I'm not certain this will work since I haven't tried it myself but it's worth a shot.