Hannebery and Shaw have been missing since rounds 13 and 14, respectively, with torn ligaments in their ankles and both – along with key forward Kurt Tippett (knee) – are pushing for a recall to face Hawthorn this week.
Jack suffered the same injury three seasons ago and compounded it by trying to make a comeback too quickly, tweaking it again.
Hannebery and Shaw are naturally desperate to regain their place in a Swans side that will carry a 12-game winning streak into this week's match at the MCG, but Jack wants both to take all the time necessary.
Preview: Hawthorn v Sydney Swans
"They've both got ankle injuries similar to what I did in 2011," Jack told reporters on Tuesday.
"I've basically told them to take a cautious approach because it is a frustrating injury and you don't want to come back too quickly and tweak it.
"It can linger around for the rest of the year.
"They're starting to run outside now, which is a big step, because it can take a while before you can really put pressure on.
"They'll train this week and test it out fully."
Hannebery took part in some light drills on Tuesday, but seems a long shot to return this week.
Shaw was involved more heavily, taking part in some short sprints, while he also failed to train with the main group.
Tippett will also need to step up his training on Thursday if he is a chance of making the flight to Melbourne.
Running laps untroubled and without any strapping on his knees, Tippett seemed in good spirits, high-fiving club doctor Nathan Gibbs and physio Matt Cameron on his way off the track before stopping for some autographs.
He also took part in some drills, but didn't feature in full match practice.
Tippett has only played five games this year due to a number of knee injuries and the club knows it is important to get him right as the business end of the season looms.
"He'll be out here today and he'll run again on Thursday," Jack said of Tippett.
"For him, we want to make sure if he comes in, he's going to be right.
"He'll be put through his paces today and if he gets through that, and Thursday as well, then we'll make a decision.
"Fingers crossed, we'd love him out there because he is such a key, but there's no point really rushing him back if he's not right."
Jack is looking forward to taking on the Hawks to get another gauge of how the Swans are travelling.
The players have an enormous amount of belief in the way they are playing, he said, but they aren't taking any interest in the winning streak, which will become the best in club history with a win on Saturday.
Jack also felt Lance Franklin would relish the occasion of taking on his old team in Melbourne for the first time, adding it was an important chance for the Swans to get some more game time at the MCG.
It will be only their third game there this season, following earlier matches against Melbourne and Richmond, with many believing the Swans will be back there for some big fixtures in September.
"We don’t get to play there a lot and we enjoy playing there," Jack said.
"We'd probably like to play there a little bit more, but the way the draw is we don't get that chance.
"So when we get a chance like Saturday night, Hawthorn at the MCG, we want to make the most of it."
Twitter: @AFL_JD
