Then now the remaining soap that i didnt wash from my hands dont lead to wrinkles ? and i have to wash my hand in normal way and dont take too much time to get rid of the remaining soap even if it is not rinsed well right ?

Correct on both: Here's what to think from now on (for anyone in such a situation): washing gently and briefly with just water is often fine. To be more thorough, or to get oily stuff off, a mild soap is helpful. One can change to a lotion cleanser like Aquanil or Cetaphil cleanser so that remaining cleanser left on the skin is lotion (is not soap). They are a good option when there's little water to wash with.