The Broncos take on Wigan at Leigh on Saturday week for a place at Wembley and Soward, signed on a short-term contract from St George Illawarra, is seen as the key to them springing an upset against the Super League leaders.
Soward, who scored a try, two goals and a drop goal on his third appearance for the Londoners in their 29-10 Cup quarter-final win at Sheffield last Friday, will miss the game against the Vikings with a back injury.
Stand-off Michael Witt (calf), captain Tony Clubb (knee) and winger Michael Robertson (hip and knee) will also be absent as the Broncos look for the win that could lift them off the foot of the table.
"We genuinely have some bad knocks," said Rea. "We're not resting anybody this week.
"Soward has travelled from Australia, he's travelled to France and we've had a long trip to Sheffield because of the bus journey.
"He's done a real lot of travelling and he's stiffened up during the week.
"Given his workload and what he's been asked to come in and do, his back was untrainable today so there was no way, given the number of miles he's travelled, that he could compete in this game safely."
Rea brings back on-loan forward Jacob Fairbank, who was ineligible to play in the Cup, and is set to give a debut to centre Ryan Shaw, who has joined the London club on loan from Swinton.
"We're a totally different team from the team that faced Sheffield," Rea added.
"Despite what everyone would think, we're massively focused on getting a good rhythm for this game against Widnes.
"The 17 that take to the field will be really clear on their mission and what they want to do as a team.
"There are some important challenges and opportunities for the guys making the squad. Some blokes will get a chance this week to say they want to be part of this team."