It kinda sounds like you are going about it in an odd way. I'll explain the answer to your question, then I'll explain a different way to do it.

In the IActionable, where you specify the NavigateURL, there is a version of the NavigateURL function that allows you to specify additional parameters in a string array. This simply puts those additional parameters back into the query string, so it would become available to the edit control.

I think a better, and more standard DNN way to do this would be to create a "edit" hyperlink, like most of the modules (check out link for a good example) use. This "pencil" icon is visible to those that have edit rights (IsEditable) and contains the ID of the item. Basically using the above method, but for a 'link' on the same row as your item.

The default behavior of the "Edit" in the Action Menu is to add a new item. I'm not saying that what you are trying to do is wrong, it just deviates from what I feel is a standard interaction. In your case, a single record, it might be perfectly suited to the situation to use the Action Menu, but if that same control ever displays multiple records, the Action menu link will be non-functional.

Check out the Links module for an excellent example of the "pencil" edit icon. I've been using that example as the basis of a couple modules for 3 years now. :)