Odd Size Stair Stringer Question

[Tom Spacer]

I know it will be against code but I have a question on a stair stringer size, codes aren't a concern. I can't find anything on actual stringer size needed. Will 2" x 12" lumber work for stringers with a 4" rise and 12" run? Undecided on 12" run, I might go 14". Would 2" x 12" work for those. Bad hips limit the rise - it's outside steps for a long time furry family member. I can figure everything else, total length, etc. - but would I need a 2 x 14 instead? Thanks