Wines was substituted out of the match at halftime with an irregular heartbeat before Port posted a 13.7 (85) to 10.17 (77) result in their preliminary final rematch at the SCG on Saturday.
The 2021 Brownlow medallist had tried to continue playing after engaging in long discussions with the Power's doctor in the second quarter.
But Wines withdrew soon after, replaced by club debutant Rory Atkins.
Wines has managed his heart condition since being diagnosed in 2022 and was last subbed out of a match in last year's round 10 win over Hawthorn.
Hinkley does not expect Wines to be unavailable for next week's match against North Melbourne.
"He's got a good handle on it. Our medical team have got an incredibly good handle on it," Hinkley said.
"We feel safe enough around what's going on, so we'll protect Ollie and make sure we do all the tests again this week.
"Past performances would suggest he'll be fine (to play North), and he's OK now.
"He was on the bench, he was happy, and he's talking normally.
"He's just a little frustrated, if I'm being honest, about what happened."
Power skipper Connor Rozee (one goal, 27 disposals) again proved damaging, so much so that Swans tagger James Jordon was moved off his post at quarter-time.
Zak Butters also dominated with 27 disposals and seven clearances.
Willie Rioli, after a difficult week as the latest Indigenous AFL star to be racially abused, kicked three goals to help keep Sydney winless at their home ground this season.
Port are 10th with a 3-3 record, while the Swans drop to 13th (2-4).
Sydney's usual stars struggled to fire, with highly-rated onballer Chad Warner taking just two touches in the first term to finish with a total of 21
Defender Matt Roberts took a game-high 30 disposals, while Aaron Francis came off the bench and kicked three consecutive goals to keep Sydney alive in the fourth quarter.
Rioli was at the source of the opening major, releasing to Mitch Georgiades (three goals) inside-50, who then spotted an unmanned Sam Powell-Pepper (two) in the goal square.
Isaac Heeney (two goals) pulled off a superb six-pointer from the pocket to reply but the visitors remained on top, enjoying a 4.2 (26) to 1.2 (8) lead at quarter time.
After losing key forward Joel Amartey (hamstring) earlier in the week, Sydney clearly lacked polish in attack.
Despite finishing with 61 inside-50s to 53, Dean Cox's men only took nine inside-50 marks to 14.
Nick Blakey had pulled off three electric runs down the corridor in the second term, but he fluffed his shots at goal.
"I said to the players, 'Did we deserve to win? Probably not'," Cox said.
"That was probably one of the lowest efficiency games we've had."
Port midfielder Willem Drew slotted a goal 10 seconds into the second half before the Swans came to life to kick three-straight majors.
Sydney came within 11 points when Hayden McLaren goaled in the 31st minute of the last quarter, but they could add only three more behinds as their comeback fell short.
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