Left-back Byrne fell heavily on his shoulder in training on Tuesday and is in a race against time to be available.
“The doc said that the next 24 hours will be crucial to see if it settles down. If it doesn’t he will be out,” said Bradley.
Though Trevor Clarke, who played left-back in Byrne’s absence earlier this season, is an obvious replacement, Bradley is wary of playing the slightly-built winger in a defensive role given the physicality of the opposition.
“We just have to be careful with Trevor because the right-sided player they have is 6’ 4” and they hit him on diagonals a lot,” cautioned Bradley.
“So we have to be very careful who we play there. They are a physical side, especially from set-pieces.”
Bradley still feels this is a tie his in-form side can win.
“We’ve been doing well, playing well, getting good results. I watched these on Saturday and I think if we bring that sort of form here we will cause them problems.
“They have two quick boys up front. They are good attacking wise, but defensively I think we can get at them.”
With just one point from their last four league games, Stjarnan currently lie third in the Icelandic Urvalsdeild and Bradley feels the sides are evenly balanced.
“I believe if we bring our best team, in terms of the way we can play, we can go and win the tie.
“We have to respect them, but try to go and score a goal. I believe if we attack the way we can we can score.”
With Byrne the only injury concern, and David McAllister and Graham Burke free of domestic suspensions, Bradley otherwise has a full squad to choose from.
Chencinski; Madden, Webster, Lopes, Byrne/Clarke; McAllister; Miele, Finn, Clarke/Meenan; Burke; Shaw.