I said I would finish my homework on time.

I said I would finish my homework on time.
“我说过我会按时完成作业”可以说"I said I would finish my homework on time"吗?
我是想确认下可以用would吗,用should应该是可以的.
注意,should在这里是表示第一人称将来,不是“应该”.