If you mean trashy in the way that a china cymbal can sound trashy, a steel snare drum with no damping would get you a long way. Tune the batter head medium loose, resonant head tight and hit off-center when you play. To reduce snare buzz get a 12-strand snare mat and loosen the 4 lugs surrounding them a little. It'll be like hitting a trash can, but (hopefully) a little more musical.
If you need a shorter decay, add little bits of damping.
Get some cheap heads and really experiment. I have one snare that I use for recording...I cut the head with a knife, then covered it all with a ton of duct tape, and it sounds awesome for one specific type of sound...kind of a crappy, really dark sound, like "thunk, thunk."