I realize this is an incredibly old question but it is still worthy of an answer.
What you are talking about isn't a User Control it is a Custom Control. What you want to do with the OutputCache can be done simply with the Context Cache.
In your code where you are getting the data and binding to your DropDownList do something like this:
List<Object> listOfObjects = null;
//assuming a List of Objects... it doesn't matter whatever type of data you use
if (Context.Cache["MyDataCacheKey"] == null)
{
// data not cached, load it from database
listOfObjects = GetDataFromDB();
//add your data to the context cache with a sliding expiration of 10 minutes.
Context.Cache.Add("MyDataCacheKey", listOfObjects, null,
System.Web.Caching.Cache.NoAbsoluteExpiration,
TimeSpan.FromMinutes(10.0),
System.Web.Caching.CacheItemPriority.Normal, null);
}
else
listOfObjects = (List<Object>)Context.Cache["MyDataCacheKey"];
DropDownList1.DataSource = listOfObjects;
DropDownList1.DataBind();