I don't think there is a way to programatically extract the SQL query. Unfortunately you will have to either have somebody do it for you or install a version of Crystal Reports. There is a free trial for Crystal Reports available from SAP here. I would download it, open the report. You can find the SQL query under the Database tab. Please see screenshot.
EDIT:
There is also rpt inspector, which will allow you to get the SQL query. They have a free trial as well here. It may give you all the info you need but probably won't let you make any changes to the report layout, if that's something you had in mind.