Answer is - use "ES Explorer"
Very strange, but "System settings" have only Ringtone and Notification, and no Alarm-clock sound. I think it is a bug. Maybe that setting should be in Clock app, but it also no.
Steps:
- Play any music file you would like to set as default ringtone for the alarm in ES Media Player
- Click three dot button [:] in top right corner
- Select Set ringtone
- Now set ringtone dialogue will open. Choose Set alarm
- Now open Clock app. You should not see the warning