One of your USB TAP debuggers is specified as being for the Hawk. So, which processors are those?
Your first link is broken, but it doesn't matter.
I decided to risk the $99, and ordered it. It works OK.
For anybody contemplating a USB TAP debugger, you set it up by selecting Edit (target) Settings Remote Debugging Connection, where (target) is the name of your project, as selected in Project Set Default Target.
DO NOT use Edit Preferences Remote Connections They offer the same choices, but only the first one actually does anything useful.
'Hawk' is the alias name for the DSP56(F)8xx hybrid (DSP+MCU) series, see:
They use the OnCE (On Chip Emulator) debug interface like the DSP563xx (Onyx) and DSP5672x series. I guess you got the 'Hawk' alias name from here:
Anyway the Code Warrior USB Tap is only usable for the speciefied MCU and the according Code Warrior tool.
Retrieving data ...