Hiren's Boot CD with UEFI support?

Short answer: No; you cannot make Hiren's Boot CD EFI compatible.

Even when Hiren's uses Syslinux and it is true Syslinux 6.03 now supports UEFI (syslinux.efi) you will face at least 2 problems when upgrading your Hiren's CD to Syslinux 6.03:

1. syslinux.efi is not an UEFI signed application then forget about the SecureBoot scenario.

2. Syslinux.efi (as the rest of EFI boot managers) can only boot kernels that were built with certain EFI parameters turned "ON" i.e.

   CONFIG_EFI=y
   CONFIG_RELOCATABLE=y 
   CONFIG_EFI_PARTITION=y
   CONFIG_EFI_VARS=y 
   CONFIG_FB_EFI=y
   

Hiren's kernel is not built with those flags "ON" and you (surely) do not have the exact sources/config for re-building the kernel while adding the above mentioned missing EFI related parameters.

Have you tried via USB with rufus? Try Rufus USB. Rufus is a utility that helps format and create bootable USB flash drives, such as USB keys/pendrives, memory sticks, etc. Handles UEFI as well as legacy booting

Important: Select "MBR partition scheme for BIOS or UEFI computer"

Link: http://rufus.akeo.ie/?locale=en_US