Players released after the trade deadline are subject to waivers, which are reserve order of the NFL standings. We’re around 26th in the order:
https://en.as.com/nfl/can-nfl-teams-sign-players-after-the-trade-deadline-in-what-cases-f202511-n/?outputType=amp
That said, maybe no one will want to pick up his contract and he will sign with us. That’s about the only way I see Cooks becoming a Bill this season.