getting the Genital warts by item contact

I have been told by my Doc that i have Genital warts. They are in treatment right now.  I was with my now to be ex wife for 11 years. and 2 other shared partners. we had.  She has tested clean for it. but i have the warts on the scrotum only on one side. there are many diff clusters  but all on the same side.    I been told by my doctors  i could have gotten this from  something like a contact souse. like the  toilet seat or  the changing benches at the workout club.   MY ex wife has said her doctor has said that  you cant get it that way.    what is the  the truth in this.   Grant you we did not break up over this matter. But to put both our minds at ease.   Also can a woman show no signs of the HPV or Genital warts  if they have it and they do a Pap test?