It should work, afaik chroot always use the binaries of the system you chrooted, so you will be able to use pacman normally. I don´t remember if chroot will mount the efi partition by default, you can do this before go to chroot (again, I'm have some memory issues but I believe that /dev does not mount as well if you just use chroot, this is why arch have arch-chroot that mounts this kind of stuff but you can mount before so it should work).

Assuming you are using systemd boot on efi partition (that is likelly if you have not changed the installer defaults), what I would do:

• On your live CD run sudo fdisk -l to get what is the efi partition, usually will be /dev/sdb1 since sda will be your usb, you should be able to see something like that.

• Then you will mount your endevour partition, in your situation should be sudo mount /dev/sdb1 /mnt/mydisk but check your fdisk command output.

• Now you will have to mount the efi partition sudo mount /dev/sdb1 /mnt/mydisk/efi

• Then you can use chroot /mnt/mydisk/ and proceed to do a pacman -Syu, this should trigger the post scripts that create the kernel images on the efi partition.