You can do this if the application's object structure does not change after you fix the bugs. Note that you need to modify the part of the test that starts your application and sets the application process's object, and refer these actions to the new program2 application. If you are using Name Mapping, you need to modify the application's process mapping criteria and change the mapped process's name to "program*" (without quotes).
Another way to make your test run with the new .exe is to rename the file back to program1.
If you face some issues, please describe your scenario in more details.