I don't ever recall hearing "worsh", rench or anything like that in the five boroughs of NYC. But some Brooklynites did "eye-ron" their clothes. Seems to be a common misconception that the typical Brooklynite speaks like the character of Archie Bunker on All in the Family - "goil for "girl", "berl" for "boil" and "terlet" for toilet, "terty" for "thirty". That did exist in some pockets and I am not sure where that came from. Some believe it is a holdover influence from a time when Brooklyn was a Dutch settlement .
Whatever it was, my parents never spoke like that - they did have a very rapid speech pattern and did drop the final "r" in some words and pronounced coffee as "cauwfee", frankfurters as "frankfooters" and dog as "dauwg".
The only laundry related pronunciations I recall were "Clorex" for Clorox - the term "Aqua Lina" was also used interchangeably with bleach. Some think it was an Italian term for bleach but it actually was a local brand, long gone. Some also used "Javelle" to define bleach. "Sta-Puf" was used to define any kind of fabric softener (also called "water softener"). And of course, Cheer was always "blue Cheer" (i.e., "run up the corner to the A&P and get me a box of blue Cheer."