Just so you know, first versions of Code Composer Studio were not free. At some point TI decided to make CCS free (CCS was mostly Eclipse+GCC FOSS software anyway, customized for TI products), and released a license backward compatible with the former paid versions of CCS v4, v5 and v6 IIRC. The universal license, same as various versions of former CCS are all free to download from the TI software archives.
So, if you find the version you need was not free, download and install it, then apply the free for all license that was released later (it's a filename called 'ccslicense.lic'). From their readme.txt:
Free license for older versions
With the release of CCSv7 all previous v4, v5 and v6 releases are free of charge.
Simply unzip and copy the License File for Older versions into
<install dir>/ccs_base/DebugServer/license
Then go to Help -> Code Composer Studio Licensing information and point CCS to this license file. Restart CCS.
Couple of years ago, I had to use a TI DSP (from the C5000 family), and the newest I've installed was CCS 4.2.4.00033 under Windows XP, which was installed in a VirtualBox machine. Keep the VM offline, with the virtual LAN cable unplugged, and never update and never download anything from WinXP. Download with a recent OS first, then manually copy/paste into the virtual machine whatever installers you may need. That will avoid any security vulnerabilities a WinXP might have, and you won't need to install a WinXP antivirus either.
I don't know about which programmer is supported, but once you have the VirualBox VM ready, you can clone the same WinXP install as many times as needed (WinXP is very small, something like 1-2GB, don't remember precisely) and install various CCS version in each clone, anew, and see what programmers they support.