Claims of a "toxic culture" at the WRU were aired in a television documentary last week, resulting in the resignation of chief executive Steve Phillips on Sunday.
An independent taskforce is to be set up to tackle the allegations, with Sport Wales, a Welsh government-funded body, advising on the make-up and remit of the panel.
Asked how clubs could be persuaded to support change, Walker said at a press conference in Cardiff on Monday: "You come up for a compelling argument for change because where we are now is not sustainable.
"If we are not prepared to change, the future of Welsh rugby and the Welsh Rugby Union is in danger. I can't put it any more bluntly than that.
"We've accepted the need for change and we want to get to that change programme as quickly as possible."
A number of former WRU employees took part in the investigation by BBC Wales.
Charlotte Wathan, general manager of women's rugby until her resignation last February, spoke of how a male colleague said in front of others that he wanted to "rape" her, while another unnamed contributor said she was left contemplating suicide by her experiences of bullying and sexism at work.
Former Olympic hurdler and Wales wing Walker, who described the allegations raised in the documentary as "harrowing and despicable", said the rape claim had been investigated by a leading law firm.
He said: "They came to a view they couldn't substantiate the claim and that investigation, if required by the taskforce, will be turned over to them so they can look at it and they can say it needs to be investigated again.
"If this person needs to be interviewed or that person needs to be interviewed, we will comply with it. We're opening up our shop, no question is off the table. They can have access to everything."
Walker wants a rapid conclusion to investigation, saying: "I would hope that it would be weeks".
