The team said the giveaway, inspired by Weiner's scandal involving salacious pictures sent online, will still take place July 23, coinciding with National Hot Dog Day, the St. Paul Pioneer Press reported Friday.
The boxer shorts, which feature an image of a hot dog being photographed by Twitter's blue bird logo, will be given to the first 1,501 fans 18 and older to arrive at Midway Stadium for a game on that day.
Officials of the minor league club said the game will also feature a photo contest with a prize of two round-trip tickets to the July 4, 2012, Nathan's Hot Dog Eating Contest in New York. Pictures of hot dogs submitted via Twitter will be shown on the stadium video board during the game and the winner will be chosen by the fans.
Saints spokesman Sean Aronson said he does not think the congressman's resignation will decrease interest in the event.
"I know we as Americans have a short attention span but I hope it's not that short," Aronson said.