With Friday night's NRL clash with the Dolphins under threat due to rain and heavy winds, Souths attempted to take a business-as-usual approach on Monday.
Walker (calf) and Graham (hand) both trained at the club's Heffron Park base, with the latter allaying initial fears he could miss the opening month of the season.
Jai Arrow is certain to return from his shoulder surgery after missing the pre-season trials, and is set to play on one edge with Keaon Koloamatangi on the other.
That will leave Tallis Duncan and ex-Dolphin Lachlan Hubner vying for the No.13 jersey, following Cameron Murray's season-destroying Achilles rupture.
"Those boys are more than capable," Arrow said.
"Tallis showed what he can do at 13, he is good with ball in hand. He is aggressive, doesn't mind the niggly and tough stuff. He will get his opportunity there.
"Lachy Hubner will be like a bull out of gate. What he brings defensively and with his energy, he will be there to be aggressive and play some footy."
Walker and Graham's participation in training on Monday comes as a significant boost to Wayne Bennett's side who have endured a horror pre-season.
Jye Gray will play fullback after Latrell Mitchell's hamstring tear ruled him out of the opening six rounds, while Isaiah Tass will move to the wing outside Graham.
Jamie Humphreys and Jayden Sullivan both trained in the halves on Monday, with English import Lewis Dodd failing to impress in pre-season trials before being suspended.
"It hasn't been ideal to lose players, but we've probably handled it better than anyone in the NRL with the amount of players we've lost," Arrow said.
"We're excited with the boys that come in and hopefully make those positions their own for the time being.
"We handled it really well. It happened in a five-minute span at training losing Cam and Latrell. We had to move on pretty quickly, and we feel like we've done that."
Souths bosses spoke with the NRL on Monday around travel plans for Friday's game, and the potential of flying Wednesday rather than Thursday.
Beyond the damaging winds, Cyclone Alfred is expected to bring daily rainfall of up to 600mm. A 2015 Test at Suncorp Stadium was postponed after 100mm of rain.
The NRL, Souths and Dolphins remain confident Friday's round-one match will go ahead as planned, with NRL officials on a flight home from Las Vegas on Monday.
But the reality is a call may be needed early in the week if the match is to be moved, due to travel difficulties caused by the cyclone.
A home-game swap is out of the question with Accor Stadium unavailable, but Allianz and CommBank Stadiums are both free on Friday night.
If both teams are in Brisbane and weather stops the game from being played, a delay until later in the weekend would loom as the most likely back-up option.
