Just for the record and I hope this helps someone.

I'm able to use distrobox/apx in Guix. I shared 4 files here that are 
required for the following script.

You will require Podman as a system package (but I think adapting the 
script for Docker may be possible) and Nix as system service-type installed.

sudo mkdir -p /usr/share/apx
sudo cp config.json /usr/share/apx/.
sudo mkdir -p /etc/containers
sudo cp policy.json /etc/containers/.
sudo cp subuid /etc/.
sudo cp subgid /etc/.
podman system reset
podman system migrate
nix-channel --add https://nixos.org/channels/nixos-23.05 nixpkgs
sudo herd restart nix-daemon
nix-channel --update
nix-env -iA nixpkgs.distrobox nixpkgs.apx
apx init --aur

Please, take in count that inside the files attached here you may need 
to change my user gus to yours in your computer.

And of course, even entering an apx container will break some 
executables in the host as well as in the guest and for that Guix Home 
is going to be required.

Good luck!