the communication with ssh protocol is secure, but i think your admins have other reasons for not granting ssh access with the first request.
when you gain ssh access to a system, you can normally copy files to the system and execute them (not only your jars). this way, you could upload files gaining root access or compromise the system in a different way.
so when granting ssh access, no matter how secure it is setup, you have direct access to the machine and this is another attack vector to the system. the philosophy should be to enable as few services as possible. but i can't imagine your admins are not already using ssh. so there should be no additional risk on enabling ssh, but perhaps on giving away a new account on the server. ask them whether they use public key authentication or password authentication. it is a good security advice to use public keys.
another reason for not granting you access, could be that they loose a bit of control over the server, because they do not know in detail what is running on the server. so tell them in detail what you want to upload and what these programs do. they might ask you some more questions or tell you you have to change something, but this way you can work together with your admins to get your jars running on the server.
as a windows client, i agree with Chris Kaufmann, putty is a very good client on windows.