Throwing weapons require only one hand to draw and throw. You can use your free object interaction at each turn to draw a new one each turn. It simply requires that you have enough to go through one or more battle confrontations.
As a thief, most of your damage will come from Sneak Attack. As a result, the smaller damage caused by the weapon will be less important. However, you must use a finely launched weapon to activate Sneak Attack. The best option for this is the dagger or dart. The dagger has the added advantage of being useful in melee, but the dart is cheaper and lighter, which facilitates its grip.
Darts and daggers have a range of 20/60. Therefore, if you throw them beyond 20 feet, you will have a disadvantage and you will lose the ability to use Sneak Attack. The solution to this is the Sharpshooter feat, which allows you to roll at maximum range of the weapon without inconvenience.
Alternative: Enter the feat of Dual Wielder
Dual Wielder's dual turn will give you a +1 AC while you carry two weapons, and you can shoot 2 weapons per turn. Have a dagger in each hand and you can attack twice per turn (once with a bonus action) for only 1 AC loss compared to using a shield. It costs a feat, but it can be a good option.