Nix is... tough. I really want to like it, but every time I pick it up I end up having to write some custom package definition for some obscure transitive C dependency with its own snowflake build system. Couple that with poor documentation for existing packages, the terrible search engine experience ("Nix" and "Nix packages" usually turn up things about Unix or "Congress Nixes Aid Package"), and a thousand other papercuts and it just seems to create more problems than it solves. I dearly hope this changes.
Guix is like Nix, but I don't think Nix has an equivalent command to bundle a bunch of packages into a self-contained file for running on arbitrary distros (without Nix/Guix installed).
Nix would be your best shot at that outside Docker.