His wife, Wendy, said the tribute was "really special".
"It's a wonderful memorial to Graham and it's also special that everybody from Cobblestones are still remembering him as me and my family still do everyday," she said.
"It's lovely they have remembered him in this way."
Mrs Croton said her husband had worn his top hat to all occasions relating to the museum so it was fitting for the memorial.
She said members from Friends of Cobblestones, a group Mr Croton founded, had recently payed her a visit and asked if they could have the hat.
"I went straight into the linen cupboard, where it was stored on top of the towels, and got it out and gave it to them."
Mrs Croton said her husband's hat had come from Wellington and "he'd had it for years and years".
"He was such a wonderful man," Mrs Croton said.
"The memory is always going to be here, which is lovely."
Cobblestones Trust chairman Graeme Gray said it was the idea of the trust and the Friends of Cobblestones to remember Mr Croton in this way.
"He always had that hat, when there were activity days, when there were visiting groups.
"I think one of the last occasions he wore it was the opening of the building," Mr Gray said.
Mr Croton's funeral service, on April 4, was held out in the open at the museum.
