I think there's a bit of mutual confusion. As far as I know, no, there is no way to do what you want without dumping. If you really want that level of selectivity, I would dump all the target stones on a tile in the same room for minimum hauling cost, and then set that tile as the mine cart loading stockpile and reclaim the stone. I personally consider dumping shenanigans to be a total pain in the ass, and only use them as a last resort.
However, everything people have suggested should give the practical results you want, even if it's not what you asked for. Do you have a large amount of unstockpiled obsidian elsewhere in your fortress? If so, why have you set up an obsidian farm? Stockpile that shit and use it. Once you do that, setting your loading stockpile to "obsidian only" will cause them to gather stone from your only obsidian source: your obsidian farm. If you are still actively mining obsidian elsewhere while farming it, you will probably need burrows to separate them, which is a total pain in the ass, and you'll probably forget to give the appropriate permissions and your legendary miners will die of no booze due to being in a booze free burrow.
I may be an exception to the rule, as I consider mass QSP abuse to be the ideal fortress management strategy, but I don't believe in having loose stone. The moment I have enough dwarves to spare, I set 3-10 dwarves with wheelbarrows to gathering up all the loose stone and putting in a tile near my stone shops. This almost totally eliminates these sorts of issues, since the only stone open for stockpiling jobs is the stuff you meant when you gave the order.