Is it permissible to put pressure on oneself and abandon caution regarding the exit of urine droplets during or after prayer, given the occasional dampness and a feeling of waswas (obsessive whispering)?

You must ignore the whispers (waswasa) related to urine droplets and not pay attention to them, for certainty is not dispelled by doubt. The default is purity, and the wetness might be from the effect of istinja' (washing after relieving oneself) or natural moisture. Ignoring the whispers is the cure to avoid the evils resulting from them.