Alarm Clock Xtreme has several options for how to dismiss and snooze alarms. Snooze can be disabled altogether, and dismissal can be set to automatic after ringing for a specified amount of time, the shortest being 1 second and the longest being 90 minutes. The default is to never auto dismiss. One manual dismiss method needs to be set as well, and the automatic dismissal happens if you don't manually dismiss before the limit is reached.
You can also set the alarm sound individually for each alarm, and if you set the auto dismiss limit as closely as possible to the length of you sound of choice, you'll essentially get an alarm that plays your selected sound once, then stops.
Alarms can be set to repeat on specific days.
I'm not in any way affilliated with AVG Labs, I'm just a happy user.
I'm using the paid version of the app, and some features described here may not be available in the free version.