Disclaimer: For unusual situations that aren't specifically covered; however, of which existing rules can be applied, read below.
If Two-Fisted Abe is simply trying to touch him, then yes of course, roll a touch attack. This would be no different from a spell caster rolling a touch attack. The only difference is, nothing happens after the touch.
It should even work with weapons. Not every attack roll has to be met with brute force.
Something similar can be seen in the movie Kingdom of Heaven; the Knight Hospitaller taps Balian on the head with his sword. He didn't cause any damage. He didn't try to penetrate armor. But he was making a point.
What is the mechanic used? A touch attack. It is in the definitions. Tell the DM, "I want to touch him to show him that I can hit him and not cause any damage." Remember Armor Class is not really hit or miss. A failure to do damage on an attack roll probably did in fact hit the opponent (hit is touch AC) but you failed to penetrate his armor, or his agility, or his other defenses (shield, natural armor, etc). A roll of a 1 is an automatic miss, because you fail to hit even his touch AC.
If One-Shot Bill is simply trying to lob an arrow without causing damage, then he can't do that with his bow. The bow sends the projectile outward and if the arrow does damage, it does damage.
A GM could make a house rule that such a master with a bow could launch an arrow with just the right amount of draw that the arrow bounces off - but that is so unlikely it would have to be a -10 minimum penalty.
There are rules for ranged pins, ranged sunders, and ranged feints, however; if One-Shot Bill was that sort of master with his bow, then he would probably have taken those feats as well.
There are other things he could do with his arrows as well to make them less lethal - fey craft, or using smaller arrows. There are also Arrows of Cure Light Wounds (whenever the arrow hits, it also heals).
Now, thrown weapons are a different thing altogether. Splash weapons are a ranged touch attack. Unless you are throwing something like a baseball at someone with the intent of really causing damage, tossing a coin or pebble at someone with the intent of it hitting their touch ac would indeed be a ranged touch attack.
Also, spitting on people is a ranged touch attack. The Eye of Gruumsh prestige class has Blinding Spittle, in which they literally spit in someone's eyes - and it's a ranged touch attack. The Spit Poison feat allows those that can deliver a poisonous bite to spit their poison instead - and it's a ranged touch attack.
PF vs. D&D 3.5e
The only difference between the two systems, regarding ranged pins and sunders and whatnot, would be CMB vs. CMD in Pathfinder which of course doesn't exist in D&D 3.5e.
Otherwise, the mechanics are the same. Touch attacks are touch attacks, and ranged touch attacks are ranged touch attacks.
D&D Glossary: Touch Attack
An attack in which the attacker must connect with an opponent but does not need to penetrate armor. Touch attacks may be either melee or ranged.
PFSRD: Touch Attacks
Some attacks completely disregard armor, including shields and natural armor—the aggressor need only touch a foe for such an attack to take full effect. In these cases, the attacker makes a touch attack roll (either ranged or melee).