Set up a script with the Open URL script step. Set it up to reference your text field.
You can place a button next to the field to open the web browser by performing this script.
You can also set up the field as a button so that clicking the field performs the script just like clicking a hyperlink, but now you can't paste into that specific copy of this field so that may not work for you unless you use a different copy of this field for pasting URL text.
Thank you, thank you, thank you! The first option (scripted text field with the button nearby) works well. Even better, I can load the individual URLs on a hidden page, then put only the active launch buttons on the visible pages---sweet.