If I understand your question correctly, I don't think there is an easy way to get it to detect what hardware it is running on and use the correct boot option. (With enough work, you might be able to, but it would be a lot of work.) You could set up two USB sticks one for each computer, or you could set it to boot the required options, but by typing something simpler -- for example, maybe "hpdc" vs "hps".
I have not used puppy, but I imagine it is using either isolinux or syslinux for its bootloader. In which case, you would need to look for a file called isolinux.cfg or syslinux.cfg. Whichever file it is, you can probably figure out what to do by studying the (text) file. If not, post it here and somebody can help you.