Similar to the 2003-2004 NHL season, only the captains wore the patch between specific dates (credit to NHLPatches.info)
January 10-12, 2003
January 11-13, 2002
January 19-21, 2001
Modano became official captain of the Dallas Stars after the end of the 2002-2003 season (July 2, 2003). While he was alternate captain before that during his North Stars/Stars years, i don't think he wore the Hockey Fights Cancer patch either in the 2002-2003 season. Dallas only played one game between the January 10-12 dates, vs the Avalanche again on January 11, 2003.