Note that there is a single-file statically linked Nix distribution now. You can get it as follows:
# curl -L https://hydra.nixos.org/job/nix/master/buildStatic.x86_64-linux/latest/download-by-type/file/binary-dist > nix
# chmod +x ./nix
and use it with a non-standard Nix store as follows:
# NIX_REMOTE='local?store=/home/eelco/nix/store&state=/home/eelco/nix/var/nix&log=/home/eelco/nix/var/log/nix' /path/to/nix \
--experimental-features 'nix-command flakes' \
build nixpkgs#hello