See also this answer of mine where I make the case It’s not the hand, but the brain.
If the brain has the circuitry to expand the body image on the fly, then any way of grasping or crudly controlling another object will be used to some effect. The evolution of grasping limbs and better dexterity in wielding will follow.
The New Calidonian crow has physical adaptations for tool use: the beak is straight so it can pick up something and hold it forward in front; the eyes can focus on the point just past the beak so the crow can easily see what he's doing. But before all that comes the mental wiring to be able to use an extension of his own body in such a manner.
My own pet, a Bronze Winged Pionus, surprised me a couple weeks ago when I saw him employing tool use for the first time. He has a hooked beak which would not be at all good in the manner of the crow’s. But he also has zygodactyl lower limbs which make excellent hands, and a range of motion that's impressive, although he has to perch on one leg to use the other as an arm.
When losing a feather, it appears instinctive that he chew it before discarding it. Some recycling I suppose. In this case, after chewing it quite thoroughly I saw him manipulating the remaining quill: holding it with the tips of the talons, the middle part of the foot/hand becomes another useful joint. He could move it to either side of his body with some surprising reach, and rotate the quill more than 180° to point in either direction regardless of which side of his body he was holding it near.
Then he proceeded to use the tip of the quill to scratch himself. Now if he was scratching himself whith his claws in the usual way, but trying not to let go of his quill at the same time, the quill would be sideways flat against his body. Instead he carefully worked the tip against the side of his head, which means holding his foot/hand at a right angle to the use of the claw; and moving it around to control the tip which is now another joint away from his actual limb.
Being able to do that at all requires the brain have the tool-feel ability.
So birds have multiple ways of grasping and controling other objects. Any slight ability in that regard will be improved by natural selection once the brain has the ability to use tools.
As for what they would do with their stone age, I think that’s defined by the natural resources. Smart tool users will find a way to hold something to further the need of manipulating natural resources. The stone age is so named because stones survive to be found; but it was also the wood age and the leather age and the leaf age etc.
The things in the natural world that are available and what physical properties they have for exploting by fairly direct modification of the original items is what will define the stone age. The species’ unique phisiology will affect the handle end of things, not the business end. They’ll make what tools can be made, regardless of what their grasping anatomy is like.