Consider the lowly sling. A couple of lengths of string or leather lace and a pouch, from which one hurls stones or cast shot.
The sling was one of the earliest weapons created by man, and it was used by regular soldiers in warfare as recently as the Spanish revolution. In warfare, the Aztec slings were considered to be as effective as the Spanish muskets.
The world record for distance with a sling is over 700 yards. In medieval and earlier warfare, archers were considered lethal to 200 yards, but slingers were considered lethal to 230 yards. Unlike archers, slingers were effective against armored troops, capable of inflicting internal injuries to the head and torso from sheer energy of impact.
Using the sling is quick ... Load, whip whip whip release.
To a student of the sling, the biblical account of David and Goliath is a classical case of never try to fight a ranged battle with melee weapons.
Slings are easy and cheap to manufacture, typically requiring about 6 to 8 square inches of leather or cloth. Old tongues of shoes are perfect.
Edit: Ammo Concerns
A couple of commenters have brought up questions about ammo.
Assuming the elves are comparable in size+strength to a 12 year old human gymnast (based on the ideal size/strength ratio for the kind of agility this lifestyle requires), they could easily handle 10 lbs of shot. Think of 12 year old boys out chasing around the forest with "kids stuff" - lunch, airsoft guns, rope, planks for a treehouse theyr'e building, etc.
A slinger encumbered with 10 lbs of 1 to 2 ounce stones for shot would have roughly 120 shots before having to reload. Their agility would only be slightly impaired.
Shot needs to have a certain mass to be effective, with different shot masses being more effective for different purposes. A 5 lb rock thrown a short distance (say 10 yards) was good for breaking horses' legs, but useless against armored humans. A 1 to 2 ounce rock hurled at much higher speed was effective at longer ranges and against armored humans. Lead shot was used by the greeks and romans to achieve an ideal balance of range and energy of impact (i.e. killing power).
Explosive shot has to have a certain mass, again, to be effective. There is a reason that hand grenades are the size they are - it's to produce enough shrapnel moving at a high enough velocity to do real damage. For reference, grenadiers in the Spanish revolution used slings to extend the range they could throw hand grenades.
Explosive seeds would be much like fire crackers. They might sting on impact and leave a welt, but would be unlikely to be as directly effective as simple stone. However, the noise could startle horses, or they could be used to set off larger planted charges at a distance.
Lower density and softer shot, such as nuts and wood pellets, will never have the range or stopping power of stone or lead shot. Getting hit with an acorn travelling at 80 mph (typical of what a 12 year old can accomplish with a sling) stings pretty badly but is hardly lethal, and something as low density as the acorn will lose energy quickly to air friction so it will have short range. Getting hit in the head, with no or unpadded helmet, by a 2 ounces of soft granite travelling at 80 mph will cause concussion. If the head is unprotected there probably also be a skull fracture, and the shot does not lose much energy to the air so it could be achieved at range..
Edit 2: Additonal information from comments
Slings were originally used by hunter-gatherers to bring down small and medium sized game animals, so their accuracy is not in question. However, it does take a lot of practice to develop that accuracy.
https://www.youtube.com/watch?v=Tpu-BCSfJ2c
(Credit @Mugluck) The accuracy and stopping power of a sling is approximately equivalent to a .44 caliber hand gun. https://www.dailymail.co.uk/sciencetech/article-4541318/Roman-sling-bullets-deadly-44-Magnum.html
(Credit @Mirror318) At release, the shot from a sling can break the sound barrier. At initial velocity of Mach 1+, shot is continuously slowing down until it hits the target, regardless of relative elevation. There is a slight disadvantage to slinging up hill, but no great advantage to slinging from above versus on the level with the target.
Side note - analysis of David and Goliath from a purely military history perspective
The confrontation between David and Goliath is mis-characterized, making David the underdog. In truth, what happened is David redefined the entire nature of that war. In the heroic age of military leadership, it was expected that the general would be the toughest fighter, and that the two generals might go toe to toe.
Goliath was looking for a man-to-man slugfest wth the Hebrew general, with the stakes being subjugation. David reframed the discussion as extermination of dangerous vermin, and changed the entire war from one of subjugation to one of survival.
David is often painted as a "wimpy shepherd boy". Based on modern day bedouin culture and the written account he was between the ages of 10 and 20 (he was too young to grow a beard).
From the age of 10, he had lived for weeks at a time in the wilderness with his sling being the only thing between having dinner and being dinner for alpha predators (lion and bear are specifically cited). As a shepherd, he had to manhandle livestock on a regular basis. Before the Goliath incident, he served as a part time armor bearer, carrying 50+ pounds of spare parts for soldiers into the battlefield while being unarmored and unarmed himself. "Wimpy" must have a really broad definition.
So, here is a famous clip that puts it into perspective ...
https://www.youtube.com/watch?v=anEuw8F8cpE
Poor Goliath never stood a chance, even if David had been a "wimpy kid" as some preachers would have you believe.
a projectile weapon is a must for a race relying on agility and dexterity rather than bulk and brute force
Why are you discounting daggers and the likes? It takes force to go through armor, but it takes dexterity to instead attack at the weak points (neck, joints, ...) $\endgroup$