@Monster Zoro's Tesla Supplier
Other than Luffy and probably Loki, no one else is getting any major fights in this arc, at this point, even Zoro and Sanji might not get any major fights either.
So no I doubt Usopp will fight anyone during this arc.
Also do you even remember Usopp past major fights?
Alabasta: A fight in which he had Chopper's help
Water 7: His fight against Luffy in which he lost
Enies Lobby: No major fights
Thriller Bark: His fight with Perona
Fishman Island: Everyone got their own fights, FI isn't really all that special, it was too showcase the SHs power after the timeskip
Dressrosa: He fought Sugar, although that wasn't much of a fight
Then there is Wano in which we thought he was going to fight and defeat Page One but we know how that turned out.
Usopp either has help or it is a gag fight with a female character, this arc is not going to be different in which Usopp will suddenly get a major fight and defeat one of the HK(Even if they are bums) in a serious 1v1 fight.
You can cope all you want, but Usopp is not getting a serious 1v1 fight against Killingham.
Even if Killingham does fully recover and somehow gets a power boost, Oda will most likely still have Sanji be the one to fight him, not Usopp.