I'm pretty sure the hegemony basically doesn't raid the free worlds League, at least until they imploded a century later. So theirs no citizens of the FWL to be found in chains in the hegemony. In fact you might see citizens working as foreign contractors for the hegemony state hired on for their expertise. In fact many hegemony nobles and FWLs citizens hang out one borders worlds quite offten. So I doubt the Hegemony would sour that relationship with raids (in fact this is outright stated in all comments on their relationship) The main thing here is that the FWL cant in good faith go against us freeing slaves, regardless of their periphery origin.
Also another thing due to nature of how hard it is to transport people, most slaves taken from outside the hegemony are either high priority targets such as techs, engineers or nobility. The vast majority of slaves are in fact natives of the hegemony itself.
According to the wiki, the Hegemony invaded the world of
Astrokaszy - which is part of the FWL - in 3035, then made another attempt to invade and conquer it in '57. To me this indicates that the Hegemony wasn't particularly averse to targeting the FWL for its raids even before its dissolution - probably through a combination of plausible deniability ("No, of
course those raiders aren't affiliated with the Hegemony. They're just common pirates, I assure you!"), and exploiting the FWL's internal divisions by essentially using its germanium-supplies to bribe the more distant FWL factions, who are more worried about outright invasions and occupations by the Lyrans or Capellans, to ignore the complains of the FWL factions closer to the periphery who "only" complain about the occasional pirate raid.
The line about the Fourth Succession war bringing new possibilities to the Hegemony by allowing for more ambitious raids also gives me this impression, since the FWL is the only of the Hegemony's neighbors who would've been distracted by it. The other neighbors - Lothians, Illyrians, Canopians - weren't involved in the 4th SW and as such the war wouldn't have given the Marians any special opportunities for raiding there.
As for the slave-taking, there's a line in the wiki about how most slaves are "prisoners of war" because it's forbidden to buy or sell a citizen of the Hegemony, though it unfortunately doesn't really indicate from what point in the Hegemony's history that is from. In general though, while people with valuable skills regarding technology, medicine, and the like would likely have been preferential targets during slave-raids, I expect the Marians would've simply grabbed as many people as they could cram into their dropships overall. You can cram a fair amount of people into a cargo-bay if you don't give a shit about their comfort, which slavers and human traffickers (which is another factor; it wouldn't just be the Hegemony's own forces going out to raid for slaves and loot, but likely also independent pirate-bands, unscrupulous merchants, etc stopping by to sell off any human cargo they might've acquired) typically tend not to. And there is a certain perverse logic to it; steal a bunch of consumer or luxury goods on a raid, and you profit once. Steal the craftsmen or factory workers who made them, and you could profit for years or even decades. Even "low-class" jobs like farmers, loggers, miners, etc are valuable in the long term by increasing your ability to support more slaves/people or providing your economy with raw materials. And those numbers would add up over the years.
If we find FWL people we could make a big show of it. Have ODRI flagged vessels bring the people we saved to the FWL captial city in a very public fashion. Should make it even harder to justify acting against us.
That's the idea, yes.

I expect we'll have to make some sort of reassuring noises at the FWL, but this sort of thing would help us keep any actual concessions/influence costs to a minimum. We might even gain some Influence, which certainly wouldn't be a bad thing, if we're looking to expand our territory a bit more over the coming years.