As planned, three people have joined the conference call at the pre-arranged time, set up by cabaret duo Frisky & Mannish's publicist in London. Sadly, it's not the correct three people. There's me up in Edinburgh, Laura Corcoran (the singer better known as Frisky) in a pub near where her parents live in Cheshire, and there's Leonie, a 12-week-old child. 'She's currently attached to my boob, so she's quite happy,' says Corcoran, the child's parent, in case that wasn't obvious.

Although it's a big bonus to have newborn Leonie joining us, and it's amazing that Corcoran can combine her two jobs as mother and comedy showgirl with such flexibility, something's still missing. 'I'm sure he'll join us any minute,' shrugs Corcoran, sounding relaxed, a textbook example of showbiz calm that amateurs could watch and learn from. Ever the professional, even while breastfeeding, she smart-casually checks her emails with her free hand to see if one Matthew Floyd Jones has been in touch.

The singer-pianist better known as Mannish, and Corcoran's professional other half, is somewhere in the Caribbean, being a kind of 'rent-a-diva' as she puts it. 'He's got a job as a stowaway pianist. He drives around the ship with this motorised piano, sipping cocktails out a coconut. He has a pop-up candelabra and fireworks with him, and surprises guests with impromptu songs; it's quite something.'

The cruise ship that Floyd Jones has been working on for the past five months (neatly dovetailing with his colleague's second to fourth trimesters) is docked for the day, giving him a chance to come onto dry land for a good signal. But something must have held him up. 'He's been off doing that for about five months,' notes Corcoran. 'I'm intrigued to see what colour his Celtic skin has gone after all that time and whether he has achieved a tan? Will it be pasty, or lobster coloured? Perhaps absolute all-over freckles?'

The results will be revealed this August when the pair return to the Fringe. Frisky & Mannish's PopLab is their first new show since 2014, a stripped-back return to the basics with just the two of them and a piano. 'Our previous shows were getting more ridiculous, I mean the last time we were in Edinburgh with Just Too Much, we had a seven-minute dream ballet sequence and tons of costumes changes. This time it's just one devastatingly glamorous outfit. And lots of fun.'

Over their ten-year career together so far, they've dipped their toes in various waters, from their 2009 debut and Fringe hit Frisky & Mannish's School of Pop, via Extra-Curricular Activities (in which they poked fun at Made in Chelsea and parodied Lana Del Rey), feminist medleys on YouTube, and CabaRIOT, their foray into political hot potatoes. 'We wrote a bunch of original songs for CabaRIOT, covering things like the queer community and social inequalities, so it was a departure from our usual Britney-focussed fare. It all got a bit heavy for a minute, and now we've swung back to the original format, just us and the piano. Doing entertainment. Or infotainment.'

The revised approach spills onto their social media too, like the Tweet on the day of Trump's UK visit which daydreams, 'imagine how much better the world would be if, instead of the news, radio stations just played 'Get On Your Feet' by Gloria Estefan every hour, on the hour.'

In PopLab, the duo will invent a definitive new pop periodic table, featuring Adelia and Selenium Gomez amongst other elements, and using science to explain various musical phenomena. 'We'll be formulating new pop compounds live in the Spiegeltent, with a fair bit of smashing together of the unexpected. Little Mix, Cliff Richard, Ed Sheeran and classic 90s dance will feature, and we think we might have found a vaccine for the contagious "tropical house" genre.'

Corcoran also hints at a section still under development, where they put pop comeback acts under the microscope, and discover a new breed of 'composite backs', such as New Kids on the Backstreet Boys. 'We're fortunate that we've been writing material together for years. Before Leonie was born, we were pretty organised and got a lot of the new show written. We'll be rehearsing it when Matthew is back from cruising, with Leonie sitting in with us. Matthew is unbelievably brilliant with babies; he has the touch, so it won't be a problem having her there.'

Corcoran is not fazed at the prospect of a Fringe comeback, this time with a new baby in tow. 'Seriously, having a baby has not been as intense as the first Edinburgh we did, and that's hand on heart true. Doing the Fringe is the perfect training, actually, for the lack of sleep, getting really good at napping, dodging illness … or not, as the case may be.'

When Frisky & Mannish first appeared at the Fringe in the Underbelly's Belly Dancer space, 'a sweaty little black cave' as Corcoran recalls, they had a great time, although she started feeling unwell towards the end of the run. 'I went to the doctor who confirmed I had swine flu and needed to be quarantined.' This time she'll be bringing a clean bill of health, a baby, her husband (Frisky & Mannish's tour manager) and her mum (the tour babysitter).

'I'm so excited to be going back. The first show we ever did got these incredibly kind reviews. The kind of stuff you dream about. But ten years on, we've had all kinds of reviews. Now I don't read them; I prefer to read the room. Our fans are super loyal and that's what counts for us. We make a point of chatting to them after and its led to some lovely friendships.'

Corcoran recalls getting a bit caught up at one point in the reviews they were getting. 'It all gets a bit navel gazey when you do that. I mean, we all know reviews are part of it, and there's this bizarre dance that we all do, but we all know it's bollocks too. We got to a point where we were almost writing songs with the reviews already in mind. We always said we'd only do it as long as it was fun. We were coming close to the edge. Luckily, we were both riding the same wave and both knew to take a step back. We had a break. And had lots of new ideas. Now we're much more about being happy, and letting that come over when we perform.'

Frisky & Mannish's PopLab, Assembly George Square Gardens, 3–25 Aug (not 12, 19), 7pm, £14–£16 (£13–£15). Previews 1 & 2 Aug, £10.