You can specify the ESXi ciphers used to serve the vSphere Client. You can do this both ways: either extend them (make it less secure, but more compatible, for instance to server vSphere Client on Windows Server 2003 / Windows XP), or restrict them to make it more secure.
VMware recommends the cipherList ALL to make it more compatible: VMware KB: vSphere Client and vSphere PowerCLI may fail to connect to vCenter Server 5.0, 5.1 and 5.5 due to a Handshake failure.
However, ALL is far too wide to be secure. Since cipherList uses the standard cipher list format documented at ciphers – SSL cipher display and cipher list tool.
You can use the cipher lists from Strong SSL Security on nginx – Raymii.org:
The Wiert Corner - irregular stream of stuff 