Lots of themes have a default Links page, so try this: create a static page called Links and see if all the links get posted there. If not, you can just copy/paste from the links widget into the visual editor as long as you make sure all your tags are closed. Then remove the Links widget.
I mean that some themes have it automatically, but I don’t think there’s an index of which ones do, so create the page and see if yours does.
If that doesn’t work, then copy/paste from the widget. Making sure tags are closed is necessary if you’re going to do this: go to the HTML editor after you’ve done it and make sure for every open HTML tag there is a corresponding closing tag. Leaving even one off can cause problems.