You really should consider changing the type of the work_date field to
date[
^] or
datetime[
^].
This will give you much more flexibility in using the data and allowing you to display the date in the format as specified by the user.
But to do what you want use the following UPDATE query:
UPDATE myTable
SET work_date = CONVERT( NCHAR(10), CONVERT( DATE, work_date, 101), 101)
First the text is
converted[
^] into a date, which in turn is converted back into a string.