Create an edge with a label and the desired visualization.
Create a user-defined palette section using yEd's palette manager (see "Edit" -> "Manage Palette").
Add the edge from step 1 to the user-defined palette section from step 2. (Right-click the edge to open its context menu and choose "Add to Palette".)
Go to the user-defined palette section and double-click the new edge template. This will set the template as the default for new edges.
You can use a similar approach for nodes as well.
This approach does not actually set the default properties for text in general, but only for the first label of nodes/edges created with the new templates. Unfortunately, yEd does not offer another way to set default properties for text in general (the above approach is the best you can do right now).