It's even easier than editing a textfile, try 'make menuconfig' in the directory, and you'll get a menu, where you can edit each setting.
This is, how I would do it (for a 184.108.40.206 kernel):
unpack the new kernel to /usr/src/linux-220.127.116.11
ln -s /usr/src/linux-18.104.22.168 /usr/src/linux
copy your old config in the directory, so you can use it as a base for the new kernel: cp /boot/config /usr/src/linux/.config
make && make modules_install
Now the new kernel is compiled, you'll have to copy it to your boot dir:
cp /usr/src/linux/arch/i386/boot/bzImage /boot/kernel-22.214.171.124
cp /usr/src/linux/.config /boot/config-126.96.36.199
cp /usr/src/linux/System.map /boot/System.map-188.8.131.52
Now edit your /etc/lilo.conf, add an entry like this above the existing image entry (make sure to change the root disk to the appropriate one):
image = /boot/kernel-184.108.40.206
root = /dev/sda3
label = slack-2.6.11
This way you can still boot your old kernel, in case something went wrong.
Run lilo as root, and all should be done.
Reboot and pray :P
Hope this helps, don't give up, if it doesn't work the first few times