I actually have a sweater worn by Fred Rogers packed away in storage. I never knew how to display it so I just packed it away when i bought my house six years back. I acquired it through Disney's "Reel Finds" shop. Not the one at Hollywood Studios (Formerly MGM), but the shop they had at Pleasure Island. They used to carry many screen worn costumes as well as personal wardrobe items back then. That shop has since closed and the one at Hollywood studios now pretty much only has autographs.
Having worked for Disney at the time, when Christmas came around, we got killer 50% off discounts on stuff in the shop, so I snagged a few costumes and stuff.
If I can dig it up I will post some photos along with the Disney Letterhead COA letter that came with it.
It stated that it was personally owned by Fred Rogers (Mr. Rogers) but does not state if it was one used on the show. It is a cardigan style like those used.