I've seen conflicting posts on this one. Some users report just setting that one layout to classic theme and others seem to need to update all layouts. It may be that it is a matter of making sure that a classic themed layout is the current layout before closing the file and uploading it to the server so that a classic themed layout is what the file is initially opened to when an IWP user accesses the file.
From there, a start up script can identify whether or not the user is using a web browser to access the file and can take the user to the classic themed layout that you want them to access.
But if if the above methods don't work for you, you might try setting up a separate interface only file for either your IWP or your non IWP users that has the needed external data source references such that the interface file accesses the tables in your current file. Then you can publish both data and interface files to the web and this interface file can have just the classic theme layout that you want IWP users to access while your non IWP users access the other interface file. Setting up such an interface file would be pretty easy as you could simply delete most of the other layouts from Manage | Layouts in that copy of the file.
This is a variation of the Data Separation Model and you might want to see this thread for an easy way to "split" a file into data and interface files: Convert to Seperation Model
Thanks Phil, a good few things to try there, although having experienced the speed I wonder if IWP is worth the trouble...