Is it possible to contract gential warts without having hpv?

In general, no...: Genital warts (like warts on the skin / mucous membranes of other body parts) are caused by infection(s) with the human papilloma virus (hpv). In the genitals, these lesions are termed condyloma. Other "bumps" can happen on the genitals that may mimic warts, and these may not be caused by hpv. If the bumps are truly warts/condylomata, then they are almost certainly caused by hpv.