Is it possible to create a custom display session that would have logic in the program script re-sort the data according to a coded SQL statement with an order by clause. Basically we are trying to avoid creating a new index and would like to be able to sort on non-indexed fields.

If this is possible, could you provide a code example?

You can use query extensions on before.program event.
Search on this forum for query.extend.where i'm sure it will help ya!

There are several threads which talk about sorting. I do not believe query.extend.where are available in 4c4 - at least not the last I checked. In 4c4 I think you will need to create the new index.