I succeeded. I didn't swap wget by curl because it is not included in Busybox. That would be the clearest solution since curl can do the same things that wget and much more.
I discovered which script is called in order to read from http and added a routine to read it from a local file with file:///.
Now my ipxe configuration file looks like below:
#!ipxe
set boot_options boot=live live-netdev=eth0 ethdevice-timeout=120 dhcp noprompt union=overlay live-getty config console=ttyS0,115200n8 console=tty0
kernel /images/vmlinuz fetch=file:////root/filesystem.squashfs ${boot_options}
initrd /images/initrd.img
initrd /images/filesystem.squashfs /root/filesystem.squashfs
imgstat
sleep 5
boot
Next step will signing up the files and add the imgverify clauses.
Is there any interest in adding that to the distro code? I would be glad to contribute with that.