I haven't read this in a long time but I don't think uke goes to look for a husband. But he does temporarily become his pet tho
https://www.mangago.me/read-manga/a_cat_s_world/
Look I could wrong.... is it Heat Stroke
I haven't read this in a long time so I don't think the uke here goes to find a husband but he does turn into a cat and becomes the MLS pet temporarily https://www.mangago.me/read-manga/a_cat_s_world/
its probably heat stroke
BL manhwa where the uke can turn into a cat and goes to the city to find a husband. He meets the seme while in cat form, becomes his pet temporarily, then runs away. Thats what i can recall of the story pls i want to read it noww(〜￣△￣)〜