You cannot normally boot a hard drive install without installing grub, unless you are booting from a boot floppy. I have, though, just found this recent thread on the puppy forum which might be worth reading:
The installer has step by step instructions and will automatically install grub if you allow it to. You can do a type 1 frugal install to a fat32 partition but I have always installed grub to a linux partition, such as ext2.
If you decide on a type2 install, I would reformat the fat32 to ext2 and install grub to it when prompted during the install. I also use the 3rd grub option to install to MBR. The puppy 2.14 manual has a useful section on installs. Get it here:
EDIT - Use grafpup pfix=ram when you boot from cd. Dont forget to take your cd out of the drive before you reboot the hard drive install. The advice in the manual on the menulst entry may not work for grafpup, but grafpup should insert the correct entry when it installs grub if you let it. You will need to apply the patch to the new install.