What about native Sql*plus spooling?
run.bat:
sqlplus hr/hr@sandbox @d:\run.sql
run.sql:
spool d:\run.log
set echo on
select * from dual
/
exit
run.log:
01:50:20 HR@sandbox>
01:50:20 HR@sandbox> select * from dual
01:50:20 2 /
D
-
X
Elapsed: 00:00:00.00
01:50:21 HR@sandbox> exit