Do I have to convert this column before the ST to a number,

A number or a string, it makes little difference

and after the ST convert it back to the DD-MM-YYYY format?

No, you just throw the sortable number/string away. Something like this:

print for map  { $_->[0] }             # extract original date
          sort { $a->[1] cmp $b->[1] } # Sort, using sortable date
          map  {
              m/(\d\d)-(\d\d)-(\d{4})/;
              [$_, "$3$2$1"]           # [original date, sortable date
+]
          } <DATA>;

__DATA__
02-02-2007
01-01-2006
03-03-2009
02-02-2009
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Output:

01-01-2006
02-02-2007
02-02-2009
03-03-2009
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