Serge and Lynx didn't switch weapons until Serge landed in the Cleft of Dimensions. Before that, Lynx (in Serge's body) wields Serge's Sea Swallow and Serge (in Lynx's) wields Lynx's traditional scythe.

Kid noticed that Serge and Lynx had switched bodies, but not until Lynx mentioned Lucca. Then, it was plain as day to her. It just didn't really matter to her, since her job was to protect Serge's body.