Hello,
Although creating drop-downs in Method Remote Entry edition is technically not possible due to the fact that creating a drop-down actually creates a new table, in this particular scenario, you're in the clear, as Method already comes with a ReportMethod table which lists the existing reports.
Essentially what you have to do is first create a drop down in a customized screen based on the "Estimate" screen, that pulls values from the ReportMethod (list of reports) table with a filter that only shows those values with the word "estimate" in it.
Lastly you would create a button (or modify the existing "print / preview" button) that would print the report as opposed to the default table.
Hope this helps.
Regards,
Denis