Swain wants Noxus to be strong, as a result, I think he respects all the other Noxian champions because they all collectively represent the might of Noxus.
Draven's a drunken idiot half the time. He's also one of the most dangerous killers in the city if you put him in a gladiatorial arena. Swain might not approve of his character and personality - but it's hard not to respect the guy who juggles axes and kills other gifted killers, with ease, all while showboating.
Darius and Swain I think are ideologically aligned and similar personalities - if Swain has anyone in Noxus he trusts - it's probably Darius or someone like him. Inasmuch as Swain is capable of trust. Darius is a skilled commander, a skilled warrior, a skilled leader, he's grim and stern and focused. He lacks Swain's intellect, but he's also naturally stronger than Swain ever was.
LeBlanc and Swain are of course at odds, but fundamentally they both want to see and keep Noxus strong. They're both brilliant, both driven, both superhuman, both vicious. LeBlanc dislikes seceding power to anyone - including Swain - and one way to potentially take back her full power would be to kill Swain. For most people, that LeBlanc is potentially willing and capable of killing Swain would make them enemies - but Swain is on his guard - and if LeBlanc is good enough to kill him - I think Swain (being Noxian) would actually respect that, and assume his death was for the betterment of Noxus: if he has a weakness and she exposes it, someone else - not wanting the best for Noxus - also could have exploited it to Noxus's downfall. Better it be her than Ionia, or Demacia, or some young upstart.
If Swain has a hesitation or distrust with LeBlanc, it's actually not because she potentially wants him dead - I don't think - it's because Swain collects information on everyone and everything. He knows the truth behind Ashe, her bow, Lissandra, etc - those are ancient secrets. He holds demonic secrets on Evelynn and Tahm Kench. He knows perhaps more about the Darkin than anyone alive - sparing the weapons themselves (certainly more than that idiot Kayn).
Information is Swain's greatest weapon - not his brilliance, not Noxus's armies or wealth, not his own demonic powers: Information is how Swain controls the empire and influences the world. And that is why LeBlanc is perhaps terrifying to Swain - because who the hell the Black Rose truly are - and who and exactly how old LeBlanc actually is - are still shrouded in mystery, lies, and overt misinformation. He is the most overtly powerful person in all of Noxus, where the Black Rose call home - and yet he seemingly knows nothing, or trusts nothing that he knows - about them. How can he feel truly in power, when in his court stands a woman who is clearly beating him at his own (information) game?
For a man like Swain, not his death or even his failure - nothing would be more terrifying - more worthy of distrust and fear, than something he cannot comprehend: that is LeBlanc. They almost certainly respect each other - but if anything keeps Swain up at night, it's those nagging questions, "Who is LeBlanc? What is the Black Rose? What do they truly want?"
Meanwhile - when dealing with someone like LeBlanc - it's probably not lost on Swain that if the overt message has been that she is likely plotting his death - the opposite is almost certainly truer (even if nothing about her is ever 'true') - that she wants to keep him in power. But why? If that is the case, is he somehow her pawn? What game is she truly playing, and against what foe if not himself?
He rules the most powerful nation in the world, and with just the slightest smirk of bemusement - she unravels his confidence without speaking a word - she makes him feel not in control - or worse - as though he doesn't even understand the game and the players. How can that be?