Omnidirectional LED, is it possible?
Telling us what you wish to do in much more detail would be helpful.


  I need that LED to be omnidirectional without using a reflector.
  Ideally it should be only one (Maybe 2 as suggested) because its power source will be very tiny (A capacitor constantly being charged by electrostatic induction), it should light an led for a brief moment.


You need to specify what you want more clearly.  


By "omnidirectional, do you mean "half a sphere (2 Pi Steradians) or a full sphere (4 Pi steradians.)  


A half sphere source mounted on a flat plane would be visible from any direction and height above the plane. 

You say "to be omnidirectional.
That is VERY imprecise 


Do you wish to be able to discern the occasional pulse by eye? 
If so, from what range. 
Or have it illuminate a volume?
If so, how large. What surface.
What brightness?

Does the illumination have to be evenly distributed across the while half-sphere or sphere?
If not, what level of 'dropoff' at extreme angles (close to the plane) is acceptable?


LEDs of the type you have shown have an epoxy resin lens. Their restricted illumination angles are mainly a result of this internal lens.  

Most surface mount LEDs have a silicone rubber encapsulant (especially higher power ones) and in most cases the radiation angle is extremely wide - often approaching the 180 degree half-sphere mentioned above. Light drops off at extreme angles away from vertical but the LED is still often visible at close to 90 degrees from the main axis.



You say "without using a reflector".
A simple 'lens' would do what you want.
A wide angle SMD LED (see below) capped by a dome of a suitable plastic (several are suitable) would give you a true half sphere emitter. Two LEDs and a clip together spherical lens would allow a light viewable from any direction. 



LEDs are (or were) available that come close to your half sphere need.

Here is an example with a 180 degree viewing angle in X &amp; Y directions.
They are obsolete, low power, inefficint and not available - apart from that one of these is visible across a half sphere and two would illumionate (dimly) a full sphere.



This 170 x 130 degree Osram LED comes close to what you want and is available.
A few in a cluster would give half sphere of full sphere output.  Output is down to 20% of max at 80 degrees off vertical in one direction and to 60% of max in the other.

OSRAM LWL28G LED
In stock at Digikey  $1.46 in 1's. 



More candidates here