Green MP David Clendon, who resigned alongside Graham, has not asked to return as a candidate.
"I've taken too many steps toward the exit to want to turn around and come back in," he said today.
Clendon said the party would be "unwise" not to let Graham to rejoin the campaign, "both in terms of natural justice and in terms of what he can offer the campaign".
The party is now considering what changes it will have to make to its campaign after Turei's departure.
Shaw said it was possible that the party's "Great Together" slogan could be dropped.
"We're looking at everything. That's one of the things that's up for grabs."
Under his leadership, he wanted the party's campaign messaging to be clearer. It would be focusing narrowly on climate change, cleaning up rivers, and ending poverty, he said.
Turei, who is quitting politics at the election, will continue to campaign but will keep a low profile, mostly focusing on her Te Tai Tonga electorate and poverty issues.
Shaw said the party was able to select another co-leader through a special meeting, but this was unlikely to happen and he would lead the Greens to the election alone.
One of the favourites to replace Turei, Julie-Anne Genter, responded strongly today to questions about whether she would seek the role.
"It's too early. Don't even think about asking me that until after the election."
The resignation of Graham, Turei, and Clendon has allowed some new candidates to jump up the list and into winnable spots. Broadcaster and sportswoman Hayley Holt has jumped up three places from 17 to 14.
However, the Greens would need to lift their vote for her to get in. Under the latest Newshub-Reid Research poll, the Greens would get 10 MPs, down from 14.
That would mean current MP Denise Roche would miss out on Parliament, and newcomers Jack McDonald, John Hart and Holt would also miss out. The party would still bring in two new MPs - Chloe Swarbrick and Golriz Ghahraman.
NEW GREEN PARTY LIST
Who gets in?*
1 James Shaw
2 Marama Davidson
3 Julie Anne Genter
4 Eugenie Sage
5 Gareth Hughes
6 Jan Logie
7 Chloe Swarbrick
8 Golriz Ghahraman
9 Mojo Mathers
10 Barry Coates
Who misses out?
11 Jack McDonald
12 John Hart
13 Denise Roche
14 Hayley Holt
15 Teall Crossen
(*Based on Newshub-Reid Research poll)