Is it obligatory to purify a doorknob after touching it with a hand that has touched drops of urine, and is it sufficient to spray it with a cleaning spray and water, then wipe it?

It appears you are experiencing obsessive thoughts (waswasa), and the effective cure for them is to disregard them and pay no attention to them. If your hand is dry and the doorknob is dry, then it does not become impure. Doubt about the existence of impurity does not necessitate purification, because the default state is purity. Assuming there was urine impurity on the doorknob, it is sufficient to pour water over the impure spot until it covers it, without wiping it, such that the impurity itself and its traces, whether color or smell, are removed.