Hi Simon,
There is no way to disable the SSL checking via Web API Services. As Eric has said, VBO is the only option you have. If VBO is not an option, you must discuss with your IT department in getting this to work for your runtime resources where the web service calls are being made.
Check the below URL if you wish to get more information on this topic via code stages.
http://stackoverflow.com/questions/22627977/the-underlying-connection-was-closed-an-unexpected-error-occurred-on-a-send-wAs I have found out, it essentially involves adding the following line (VB.NET) before sending out your web request.
System.Net.ServicePointManager.SecurityProtocol = Net.SecurityProtocolType.Tls12