Ex-St Helens flier Swift came off in Monday’s 27-10 home loss to Catalans Dragons with a hamstring issue but it is not duly concerning his head coach.
As the Black and Whites look to recover from only their second loss of the year, Hodgson said: “He seems to be okay.
"It was more of a precautionary interchange really.
“We moved Cameron (Scott) there because Swifty's hamstring tightened up, but we're confident he'll be okay for this weekend.
"Bowds should be good for next week, and if not then, the Challenge Cup semi (against St Helens).
“He's progressed really well with his elbow.
“He's been doing a lot of training and he'll be back with the team probably at the back end of this week.
“It just seems to be a bit too soon for the game, though."
Bowden, 29, injured his elbow against Wakefield Trinity last month and it has caused front-row issues given England prop Scott Taylor and Masi Matongo are also still on the sidelines.
"Tag (Taylor) is still at a non-weight bearing (stage) with his foot," explained Hodgson.
"He had a couple of fractures in there, so he looks like he's still another six or seven weeks away.
“And Masi is still a couple of months away too, after a full repair on his meniscus.”
One-time England international Shaul, of course, has not yet played this season after ruptuing his ACL last term.
Since then, the two-time Challenge Cup winner has lost his No1 jersey to Jake Connor, the mercurial talent who has thrived in his new role this term.
Asked where Shaul will fit in when he does return, Hodgson replied: "He'll be competing for playing in the 17.
"There's no doubt about that.
"And I know how good Jamie’s been in the past, and how good he's going to be in the future.
"He will still have a big say in what we do this year.
“Jamie’s a great kid, he’s working hard, he's invested in what we're doing so the sooner he's back fit and raring to go for us the better we'll be as a squad.”
Hodgson does not expect to see him until July at the earliest.
"Jamie’s doing really well,” he said.
“He's on track with everything we've asked of him. I still think it's a good couple of months off.
"Everything with knee reconstructions, there’s always three or four steps forward, and then maybe a step sideways or slight step backwards. “But we're happy with the progression of what Shauly’s done, and hopefully everything will go smoothly from here."