Australia captain Tim Paine won the toss and elected to bat against England in the first one-day global at The Oval on Wednesday - the tourists" first worldwide match since their "ball-tampering' series in South Africa.
'They don't have to do it but it's something we want to bring in at the start of a series, not before every game, ' said Paine, of the handshake idea.
'I'm absolutely happy with that, it doesn't bother me, ' said Morgan.
Ashton Agar says he's delighted banned former vice-captain David Warner's been given the chance to commentate on Australia's ODI against England at Cardiff.
England vs Australia Live Cricket Score 1st ODI Live Streaming: Australia will be eager to perform in the first ODI against England, a match that is their first worldwide game after the ball-tampering controversy in South Africa.
Warner was banned from Australian cricket for 12 months for his role in the ball-tampering scandal alongside captain Steve Smith and bowler Cameron Bancroft.
Morgan told the BBC: "We play our cricket pretty hard, positively and aggressively, so we'll continue to do that".
While England reflect on the defeat to Scotland, the series is a huge one for Australian cricket. "It doesn't bother me", said Morgan.
"We've spoke about all of this (culture change and player behaviour) over the last few months, and we are aware that words are only words", Paine said.
"We'll be judged on our actions going forward and it'll be plain for everyone to see". "It's just living our actions, we've spoken internally about our values as a team and how we want to be perceived by the Australian public and by the cricket public in general".
Eoin Morgan's England side, who are top of the world ODI rankings, will aim to bounce back from Sunday's humiliating defeat against Scotland while Australia look to restore pride after the ball-tampering scandal in March.
"So for him to be back around the game he loves is only good".
It is a match that pits 2019 World Cup hosts England against title-holders Australia. "You get to number one and people are going to want to beat you, but you want to be number one in the world".
England enjoyed a 4-1 series win over Australia "Down Under" earlier this year but will be confronted by a new-look side in London.
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