First, a return to Obsidian blades. Most close quarters weaponry (swords, axes, daggers... maces, flails, clubs) rely on a forceful strike. Not gonna be easy in zero gravity, where a lot of the power of the strike would be spent pushing combatants away from each other. Unless both were well braced, the blow will not do much - for the same reasons turning into a blow makes it much less effective.
The other thing that can do damage is sharpness. A very sharp knife can slice even with very little force behind it, from the sharpness of the blade and simple lateral motion. It is the same technique that people use to cut delicate foods in a kitchen, gently drawing the knife across and letting the sharpness of the blade do the work. I can press a blade down onto my hand with some force and escape injury, if it doesn't slide sideways, or flick it across and draw blood. Much less effort to create an injury by flicking, than by trying brute force or grappling when force must act on both parties.
The major advantage of metal blades over stone is the resilience. Stone will shatter under force, maybe even if it is dropped, it is brittle. Metal is duller, and must be often sharpened to take an edge, but it can take more force, and be repaired if it gets dented. With much of the force taken out of the question (even dropping is unlikely to break without gravity's acceleration) I expect the greater sharpness - and obsidian is much sharper than steel - to weigh heavily on what makes an effective weapon. if two people are relatively close to each other, one can lightly draw an obsidian weapon over the other to cut into them, without the force of the blow forcing them apart.
So I would expect delicate precision to trump forceful blows in close combat - they're more efficient at injuring the enemy, instead of tumbling the opponents all over the place. A few ounces of force to swipe and land a cut, instead of shoving and tumbling away to give a bruise. Short to at most medium length blades, and as light and maneuverable as they can be made would be best, since you need the fine control a lot more than the momentum from a heavier blade and reach from a longer one.
Projectile weapons like arrows should still work, they injure by speed and sharpness, and the force that gives them speed is in the flexibility of the bow and the leverage between the arm and body of the archer. I expect aiming will be trickier, as people are floating around, but there's no reason the weapon won't work. Throwing knives might be trickier, they would need more force to give them speed, in order to be effective.
But really, one of the best projectile weapons would be blowdarts - they would be murderous in this kind of setting. Their speed comes from the breath and pressure building against the pipe walls, so they don't depend on their user finding good leverage, and if the darts are sharp they can penetrate quite deeply (like, a quarter inch into wood, which is much harder than people). Even plain darts can be dangerous if carefully aimed (deadly aimed at eyes or throat, still quite serious aimed at belly or various soft and squishy places on a person), and such darts were often poisoned for fighting or hunting with. Longer pipes mean more accuracy over distance on earth and less maneuverability up close, but without gravity to warp the trajectory I expect even a shorter blowpipe could be quite effective. Remember dodging can be quite trick if the target isn't near a wall.
Weapons with cords, like flails or whips or bolas, or even simple slings - I'm not sure. On the one hand, they can extend someone's reach and can probably be given extra force through body-generated momentum. On the other hand, without gravity I'm not sure if the momentum will build up or dial down. A sling, for example, can be given a lot of force by spinning it around before letting the stone fly - but without gravity to pull it down, or out, or away from the swinging hand, making the cord tight enough to move all parts of the weapon, it might just rotate without gaining speed. Same with a bola, swinging sideways. I'm imagining a forceful swing that travels down the line and twitches the weight on the end. So, might be excellent, might flop - I think a shorter cord might work better, since all the force has to come from the hand or arm and its more controlled, so it is much less of a force multiplier than if a longer cord will work. Maybe the ninja-style kunai which can have short cords attached, or short lines with grappling hooks.
Leverage. Well, hand- and foot-holds are well and good if one is near a wall, but combat probably shouldn't depend on being near one, when someone's life is on the line if they're not. I suspect there will be grappling lines of some sort, maybe swung (if the longer lines can be controlled), maybe shot out - a mechanism like a crossbow might work if a grapple gun is not allowed, or maybe simply thrown like darts. Depending on the material of the walls, this be something sharp to dig in and hold, or something very adhesive to stick fast.
The line can then be an anchor-point to the nearest wall, used to dodge or navigate by adding sideways momentum, or directly used in combat by being landed on a person or object to capture them and drag them back, tangle them in the lines, slice into them if sharp or get adhesive over things if sticky (like landing on the junction of a weapon sheath so the weapon sticks to it). Given their use, I would expect people to have several such lines available for normal navigation as well as combat, and because retrieving them might not always be feasible, someone cuts the line, someone needs to maneuver and drag their opponent in, etc.
I'm not sure about formations and such, I expect everyone would need a lot of room until they know how this kind of combat works. There will be a lot more movement as fighters drift around, bounce off walls and each other, keep moving till something stops them. Maybe they could work in pairs or trios at most, so they can use each other for leverage and watch each other's backs... but more than that would have a really high chance of fouling each other up more than helping.
Someone might be able to brace more people in a smaller place, or tether people at intervals to a wall if they're on the defensive, know or can modify the space. A knowledge of local leverage could make them mobile within their little areas, letting them work together more densely, and if they've got projectiles, they can produce something like mass fire, and it could be quite effective at defending a space... but they also can't dodge too much to avoid any return fire, and if the enemy gets too close to their position, that bracing in will make it harder for them to get out and avoid being trapped.