Named styles are only implemented for ‘Draw’ and ‘Impress’ presently. If you create your drawings (shapes, groups of shapes) in ‘Draw’ and move them to your ‘Writer’ documents later, you can define a template for ‘Draw’ containing the styles you want.
A different line width for the ‘Object without fill’ style would apply then to any object of the class you create. You can also create hierarchies of styles and apply one by doubleclick to the selected shapes.
You may also want to study the enhancement request tdf#89369.
Editing with respect to the comment by the OQ below:
Presently there is no way to do what you want as no styles are implemented for shapes in ‘Writer’. There also is no document property like “default line-width for shapes without a fill” in ‘Writer’ (and it would be against proven principles if existing).
The only workaround I can think of is to make a document template containing prepared shapes having set the basic properties you want to set again and again. You then can create new shapes as copies from those examples and adjust the additional properties as needed. This would replace insofar the creation of shapes by using the respective tool from the ‘Drawing’ toolbar.
Edit 2:
A workaround probably superior under realistic conditions is given by @PYS in this comment on the above mentioned bug/enhancement.
I want to add that the properties to apply by the already chosen but not yet used tool for drawing a shape can also be changed without the second toolbar ‘Drawing Objects Properties’: Before the first usage of the chosen tool rightclick somewhere in the working area and the respective context menu will open, allowing you to make changes that will persist for the session if not changed again.
Edit 3 reinforcing what was added by “Edit 2”:
This proceeding is actually usable without any relevant complications.