Don't worry about re-creating the control file.

By "move the database", I mean copy the files from server1 to server2 in the same location. For example, copy /u01/oradata/sid/data01.dbf from server1 and place it on /u01/oradata/sid/data01.dbf on server2.

If you can not move to the exact same relative location, you can start the database in mount mode and rename all the files from their old location to their new locations. For example, if you had to move the above file to /u02/oradata/sid/data01.dbf you would use:
# svrmgrl
SVRMGR> connect internal
SVRMGR> startup mount
SVRMGR> alter database rename file '/u01/oradata/sid/data01.dbf' to '/u02/oradata/sid/data02.dbf';
SVRMGR> alter database open;