The usual way to display your Blogroll (list of links) in WordPress is using widgets. These can be placed in a sidebar or footer, depending on what your theme allows. There are other WordPress options though.
Kathy’s Bookmarks uses a custom template. Creating one may be easier than you think, just copy and edit one that is already associated with the theme you use. Be sure to edit the description so that you can identify it in the Template drop-down list. Check whenever you do WordPress updates and upgrades, you will probably need to upload your custom file again, but that may provide the incentive to create a child theme.
Using a plugin, such as Links Library is convenient too. It has a lot of features that you may alter via the Dashboard. Plugins (notification in the WordPress Dashboard) do need to be updated periodically but they should survive WordPress upgrades and updates.
The old static links page is available for viewing too, although I am no longer updating it.