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Small kamikaze drones launched from a safely out-of-view location?

For a 'small' kamikaze drone, I'd recommend experimenting with lighter-than-air flight -- balloons/blimps. You could make a small radio controlled blimp with significant lift capacity for far cheaper than you could build a quadcopter-style drone with the same payload capacity. And they should work well as long as you're not dealing with excessive wind.

And your balloon/blimp can be filled with cheaper, more effective hydrogen rather than helium (much more expensive and less lifting capacity) or hot air (much less lifting capacity). Since it's meant to be disposable, nobody cares about the risk of it catching fire and burning/exploding. Hell, that might actually contribute to its destructive capabilities. Hydrogen is so easy to get that you can feasibly just make it yourself with simple hardware store parts.

You don't need fancy control electronics, either. Any toy RC car's parts could be repurposed for it, including battery and motors.