Hi,
I have done something similar (install second kernel, make initrd image) but different (Mandrake, GRUB bootloader), so I will make an argument by analogy.
The only configuration file I had to edit was /boot/grub/menu.lst, which is a menu of options to boot. The analogy, I believe, would be /etc/lilo.conf for lilo bootloader. I just followed the syntax of the original kernel entry and changed the numbers/names to suit the new kernel. You also have man lilo.conf for syntax.
I needed an initrd because I was using reiserfs and this aspect of my kernel required the initrd so I had to make one. If your original kernel requires one, it will be in /boot and, if your mykernel has the same function(s) that make(s) your original kernel need an initrd, you will need to make one.
From man mkinitrd:
mkinitrd [-fv] [--with=module] [--preload=module]
[--omit-scsi-modules] [--omit-raid-modules]
[--version] [--fstab=fstab] image
kernel-version
I think what you would do, in /boot, with your mykernel image in /boot is:
# mkinitrd --ifneeded mykernel.img mykernel
and add the entry to lilo.conf.
There is also
HOWTO stuff about this at Tom Berger's MandrakeUserOrg Doc Section that might be close enough to what you need to help.
Good luck.
Eh?? What??? You want mkbootdisk???? oh.
Well, I've never done that but, since I'm here anyway, I'll carry the analogy one step further and suggest (might as well be in /boot):
# mkbootdisk mykernel --mkinitrdargs --ifneeded mykernel.img mykernel
I'll go quietly, now