What kitty litter are you using? My cat's litter is made from clay as far as I can tell...
Many cat litters are clay but that's not the right stuff. You want the crystals that are porous silica.
I use 'Mimi crystals' from Walmart for around $5 for 4 lbs.
They will need to be acclimated/adjusted to your target RH. This is a simple procedure where you add or remove moisture to achieve a specific rh.
Place the crystals in an open container or flat pan and use a good amount. (you can't use to much) and place it in your humidor along with a calibrated hygrometer and all your cigars. The more mass the better. Don't open the door for several days.
If the rh is too low use distilled water on a damp paper towel or damp sponge and place it the humidor and let the moisture evaporate into the air. The crystals will absorb the moisture from the air. Repeat if needed. It will take several days but the rh will rise slowly and safely. Take your time as there is no rush. Never apply water directly to the crystals! They don't like that.
If the rh is too high you need to remove moisture from the crystals. Remove the crystals from the humidor and place them in an oven at a low temp to dry them for an hour or so. I like to put them in a bowl and microwave them. One minute blast and then remove the bowl and stir them with a spoon and watch the steam evaporate into the air. Repeat this several times or until no more steam is visible upon stirring. Let them cool to room temperature and place them back into the humidor. The micro pours will be thirsty sucking in the moisture from the air pretty quickly.
Once the rh becomes stable the crystals will then be acclimated to a specific rh. They will add and remove moisture and help to retain that rh. Sometimes small adjustments must be made but it's very easy to correct. If you need further help let me know but it's an easy procedure that works very well.