FOUND grey cat!

FOUND grey cat on the East side of Wichita. Confirmed no microchip. All the posts I’ve made across the web are not getting any hits. I’ve recused 3 cats & sadly cannot take in anymore! All local recuses are seemingly full. I do NOT want to take him to Wichita Animal Services as they euthanize within 3 days, to my knowledge (correct me if I’m misspeaking). What are my other options? I will pay for neuter/chip/vax if that means he can get into a shelter to find a great home.