I have used MacPup and liked it, but as an alternative to puppy, I highly recommend the Rescatux/SuperGrub2 CD.
I think that is a tool that everyone should have in their toolbox. It does some amazing tricks, and has the LXDE desktop with the PacmanFM file manager which will do what you need.
It is a 389.5 MB download.
It will even load those .iso files you have from the hard drive.
Boot the computer with the Rescatux CD. When Rescatux starts you will get a menu to start Rescatux or SuperGrub2.
Chose Rescatux. That will give you the LXDE desktop (with the Rescatux program open, but you can close that).
Use the file manager to create a directory named /boot-isos on your hard drive, and move your .iso files into that folder.
Then reboot the Rescatux CD and this time chose the SuperGrub2 option from the menu. After chosing SuperGrub2, the next menu will give the options of booting any installed operating system on your computer ("Detect any Operating System") or any loop mountable iso files ("Detect loop bootable ISO's"). When you chose the "Detect loop bootable ISO's" menu item, the program will search all of your drives and partitions for the /boot-isos folder and create a menu for you that will allow you to boot any one of those .iso files. It will be a slow process to search your drives and create that menu, so be patient and let it complete.
They will run just as if you burned them to a DVD and booted it.
WARNING: if you boot a .iso for a distro like Linux Mint 17.2, for example, you can use that in the ordinary way to install Mint to the hard drive, but you cannot install Mint to the partition where the /boot-isos folder is, because that partition is mounted. You can't unmount it because that is where your operating system is (the Mint .iso)
So you have to create the /boot-isos folder on a partition where you do not want to install the OS. (It can be on a USB flash drive.)