NMR: Lucy Moment~How to remove pollen from Graco Quattro stroller?

LucyRicardo3

I've had my Graco Quattro Tandem hanging on a bike rack hook in my garage for months. The other day, I was taking my oldest to an orthodontist that has a tiny office and knew my SBS would be a tight squeeze, so I got out the tandem and used it.
 I was in a huge hurry and noticed it was very dusty and quickly wiped it down with baby wipes. We make it to the orthodontist and I was horrified that it still had a yellow powdery appearance on the canopies and the basket below.
Baby J and I both have been sneezing and coughing like crazy ever since, as if it were spring all over again! (I'm in Georgia if that explains anything.)
Ok, so has anyone ever had to scrub a stroller? This stuff is stuck pretty well! It doesn't have a musty smell, so I don't think there's any mold or mildew.
I can't use bleach for 1) it's a black stroller and 2) strong fumes for numerous health reasons.  
Do you think 50/50 white vinegar spray or just some good ol' Dawn in a bucket of warm water?  My pregnant olfactories are in over drive so Simple Green isn't an option, either.
Of course, it's mostly the fabric parts that are not removable from the stroller frame, or I'd just throw it in the front loader washing machine
Thanks in advance!