Procuring Chometz on Pesach is an Issur miDeOrraisso, whereas going into a swimming pool or Mikvah on Shabbos is at most an Issur meiDeRabbonon and probably even less than that:- Albeit squeezing water out of your hair could be more severely Osssur.
But given that the Bronx Zoo is gratis on Wednesday, and there won’t be a Wednesday during Chol haMoed Pesach this year, how about waiting until Chol haMoed Sukkos when there will be a Wednesday on Hoshana Rabba, when Bronx Zoo is gratis.