Retrospective magnetic snaps insertion

So I’m almost finished making a school days coat in a thick acrylic. Today I finished hand sewing the lining and was ready to do my last step of sewing on the patch toggles when I realised I hadn’t inserted the magnetic snaps on the inside of the facing. D’oh! So my question is: if I interface a piece of cotton and push the snaps through that and stitch it to the facing, will that work? Will the cotton be sturdy enough to withstand regular opening and closing? I've attempted to attach a photo.