I suggest you create an additional cpio archive (newc format) which
just contains the filesystem.squashfs file (in the appropriate folder)
and nothing else.
Now you have multiple options:
1. Most bootloaders have an option of specifying more than one file as
initramfs; just try adding your cpio archive as a second file (check
your bootloader's documentation).
2. Alternatively you can compress the new archive and append that to
the existing initrd, using something like
gzip --fast -c YOURARCHIVE.cpio >> initrd.img
3. You can do the same as (2) without the compression (which makes
more sense since the squashfs file is already compressed), but then
you might have to add null bytes to initrd.img first so the archive
is properly aligned (see [1])