You could use Schema.getGlobalDescribe() and see if the History table for the correspoding object exists.
Map<String, Schema.SObjectType> sch = Schema.getGlobalDescribe();
System.debug('Contains Account History');
System.debug('Contains Application History');...
For anyone looking at this in the future, this post has solved my issue: StackExchange Post. You need to set your site name as your as the user name and it will show up in debug logs (without setting a cookie).