If you donít have a mixer, you are likely to have a very hard time making a dough for a thin and crispy pizza, if by that you mean a cracker style pizza. Many recipes I have seen on the forum for cracker style doughs call for so little water by weight in relation to the weight of flour (under 40%), that unless you have the arms of Popeye and the strength of Hercules, you will be unlikely to be able to hand knead the dough because it will be very stiff, dense and dry, and often crumbly to boot. If you somehow managed to hand knead such a dough, you would also find that it will be very hard to roll out when you are ready to make pizzas because of the low hydration of the dough.
If you have a food processor, that may work but most of the cracker crust dough recipes I have seen on the forum that permit the use of a food processor also call for use of a cutter pan (or some equivalent like a perforated pan) as opposed to a stone to bake the pizza (see, for example, http://www.pizzamaking.com/forum/index.php/topic,779.0.html
, and http://www.pizzamaking.com/forum/index.php/topic,1311.0.html
). You might try using a food processor and the baking stone approach with one of the above (or similar) dough recipes, but I donít know how well that will work out.
If you donít have a food processor either, the only other option that comes to mind offhand is to select a cracker crust dough recipe that calls for more water in relation to the amount of flour. Or else you can keep adding water just to the point where you can hand knead the dough. I think you would need at least 50% water by weight of flour, and perhaps quite a bit more. In that case, you most likely would have to dock the dough once it has been rolled out and pre-bake the rolled-out docked dough on your new pizza stone before adding the sauce, cheese and toppings (sparingly) and finishing the baking. I described a recipe with 50% hydration at http://www.pizzamaking.com/forum/index.php/topic,5173.msg43956.html#msg43956
, but I was not using hand kneading so I canít say for sure how much effort it would take to do a hand kneaded version. It may be possible but unlikely to be easy. Maybe you can be the one to find out for us.
I am not all that knowledgeable about the cracker style pizza (I am still learning) so you may also want to scan the index for the cracker style at http://www.pizzamaking.com/forum/index.php/board,28.0.html
to see if you can find a recipe that more closely fits your circumstances. Or perhaps a member more knowledgeable than I can suggest a simple "foolproof" recipe for you to use if you are hand kneading and want to bake the cracker style crust on your new stone.