I don't know if it's so much stank, but stain. Some of the rubs with paprika, chili powder, etc., that can seep through peach paper with any juice/grease will put some stain on that's very hard (if not impossible) to knock out. My advice (unless you're cooking for the Packers, Texans, or Patriots) is to go to Wally, spend around $15 on a 48 qt. Igloo/Coleman and call it yours and yours alone for smoking. Think about what the biggest thing you'll likely cook that needs a cooler and back into it--typically a brisket or turkey, and get measurements for your cook purposes. You don't need an RTIC/Yeti/Pelican, nor a 128 qt., for something like this, and you don't have to work around the missus on retiring one she likes and drop a bunch of change and time on a new one she does. This one is yours and yours alone for the smoker for under $20--period. While you're at it, go grab a couple of inexpensive Wally towels for another $5 and call it a day.
Now, if you take those grease-laden wrap towels, and toss them in with her unmentionables to wash, then you're on your own, hombre. Can't help you there. :ROTF