Girl Thing member Linzi Martin claimed on the ITV2 show that she co-wrote the verses for Hear'Say's breakout hit and recorded backing vocals, a claim backed up by bandmate Jodi Albert in her blog for Digital Spy and Klass herself on Twitter.
Speaking to DS, Shaw - who exited Dancing on Ice this week - said that she wants Girl Thing to have a hit with the song that launched her career.
She revealed: "It's funny, because the vocal coach from The Big Reunion said... 'I'm about to go in with Girl Things to do the harmonies - we're struggling. Where did you place your harmonies?' So Myleene and I racked our brains... and we were helping them out."
The star added that she cannot be sure of the accuracy of Martin's claims, but knows that redistributing songs is industry standard, as Hear'Say originally recorded Lemar's song 'If There's Any Justice'
"I don't know whether they wrote it. I wasn't under that impression, but maybe it was - I know what the industry is like," she said.
"We recorded 'If There's Any Justice', which Lemar got a number one with. That was originally our song... they decided it was too mature for us. So, I do know how it works, they could have helped write it."
Asked if Hear'Say's version of 'If There's Any Justice' still exists, Shaw replied: "I have it. Maybe one day I'll release it. I might put it on YouTube and put my own video to it."
On whether Hear'Say would ever go on The Big Reunion themselves, Shaw replied: "From our perspective, Hear'Say was a really small part of our lives, what is the reason for going back?
"It wasn't right for any of us. There was not one person going, 'We should be doing it'. There was no split decision, it was all very amicable when it came to [deciding], 'No, it's not for us'. I think that's the right thing to do."
The 32-year-old also announced that she is working on a new '80s sci-fi musical set in a high school with A1 singer Ben Adams.
"In two weeks we're going to sit down for a whole week, lock ourselves away, work on the musical and see where it goes really," she said. "It's such a fantastic concept.
"There's] many opportunities, it can go from being a musical, to a series, to a movie."
Shaw was speaking to promote her role as patron of The Brain Tumour Charity, which aims to shorten diagnosis times for childhood brain tumours. For more information visit www.thebraintumourcharity.org.