The best replacement for swiffer is mop.

The best alternatives to swiffer are rated as following:
★★★★★  mop
★★★  shark
★★★  bona
★★★  broom
★★  vacuum
★★  clorox
★  dyson
★  clorox ready mop
★  dust mop
★  clorox mop
★  libman
★  microfiber
★  pledge
★  shark steam mop
★  steam mop
★  rubbermaid
  readymop
  vileda
  floormate
  casabella
  wetjet
  norwex
  pledge duster
  swifter
  feather duster

Your alternative for swiffer is not listed? Suggest!
Speaking about swiffer, one probably shouldn't forget about bissell.

Other search terms related to swiffer and their ratings are:
★★★★★ bissell
★★ vac
You have in mind a companion for swiffer and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of swiffer in all years. Click on graph for more.
swiffer
mop
shark