An annular snap fit using inflexible material such as stainless steel (or aluminum!) will require a yield point in the ring.
Allowing that any ring you can design will be a non-zero thickness cross section of a cylinder, the resulting item will resist compression (internal snap component) or will resist stretching (external snap component) and require excessive force to assemble.
Such assembly will likely damage one or both components. Disassembly will likely damage one or both components.
Consider to provide a slot in one or both components, allowing for compression of the inside portion or expansion of the outside component.
A common implementation of such a design is called a snap ring or circlip. This is a C-shaped piece of metal designed to engage a groove in another part. The metal is often a stamped out (cut/sheared) ring which will distort in the plane of the sheet when "stretched" open to engage the groove.
You would therefore have to allow for such distortion in your design by providing for such flex, although I am uncertain of the direction of flex if your C-shape uses cylindrical cross section.
The image below comes from a commerical web site for this type of product:
Some of the rings have a proportionally large gap, while others are designed to close completely but allow for spread during operation.