er..My floors get the swiffer wet mop,with chemicals on some, sometimes when you use the swiffer mop you find you can use 2 clorox chemical wipes on the pad and mop with them,but if the windows and doors are open this can get out quickly..
People in my house do mopping in sections,so hallway+ kitchen,bedrooms+ bedrooms,kitchen/dining room+ living room,so the smell doesnt overpower anyone. But the chemicals in the wipes are transfered on to the floor and the smell isnt strong unless you put it within 2 feet of yourself.These have been used usually even near my bird cages but because these are high up around 3\4 feet off the floor on tables,or at times moved to another section for say cleaing the table too.Just be careful how you do it near the birdcages,and dont let any pets on those areas till long after they've dried
now for the slightly more bird friendly way, (
check it out)recently I've been using this steam mop,just add water plug in and hand pump,and it'll make floors shine,and has like 5 different mop heads even a steam duster attachment.
You just sweep/vacuum then go over it with the steam mop, it's about the size of a hand vacuum+ the 4 foot pole/handle(no i'm not trying to sell you one

),the noise of steam comming out is identical to Darth Vader....and on an average it takes like 10min to mop a large section of an house and sounds like Darth Vader running a marathon/asthma attack.
This can cause some stress at first to birdies but it's amazing and makes you want to roll on the floor, and immediately after the wetness has turned to vapor i've been having a hard time resisting the urge of letting my budgie play on the floors with me.