I just changed my 21 Ubers to a new set of rims and winter tires. I never had that special tool either, but a wire coat hanger (a thicker one) worked for me, pulled those center caps off very easily.
Biggest problem I had was getting my jack + puck under the car, car was too low, I had to drive up onto some pieces of wood to get enough clearance. And if you are installing new TPMS, you will probably need to drive about 5-10 miles to get new TPMS to register, report the correct pressure and align to the correct location.