This is strange, because RC4-SHA is in the default cipher set used by IO::Socket::SSL on the client side (but only as the last choice). This must be a very strange SSL server you have there, could you share some details about it? (I'm the maintainer of IO::Socket::SSL and always on the search for unusual SSL issues.)
Sure. The server I was connecting to was the Unifi AP controller - Unifi AP - from Ubiquiti Networks. This link if for 2.4.6 but I was using the beta 3.12 (and 3.10) versions. I am not sure if that is what you are after but let me know if I can get you any other information.