I'm making a cookie cutter model to 3D print, and I want to extrude the upper ring of faces to be wider on the top (or just make it thicker on X/Y axes)

I've tried selecting the upper ring and separating it, then applying solidify modifier and later joining both meshes with CTRL+J into one. It looked kind of like I wanted to, but as a side effect I got a few unfixable non-manifold edges so in the end my 'solution' was garbage. Any other ways?