Where can you kayak in the swamps near New Orleans?

Yes, New Orleans Kayak Swamp Tours, a tour company in New Orleans offers 3 types of kayaking tours:

1. Manchac Swamp Kayak tour - a 2-2 1/2 hour tour
2. Honey Island Kayak Swamp tours - a 2-hour tour
3. New Orleans Plantation Tour & Swamp kayak - an 8-hour tour 

Get the details on their website.
A fun tour to check out is the Swamp Landscape Photo Workshop by Wild Louisiana Tour. It's a kayaking tour guided by an experienced nature photographer.

We used Wild Louisiana because we wanted to avoid some of the environmentally irreponsible tours that feed to crocs and we wanted a naturalist to lead the tour. We did the Manchac tour and it was awesome. Have fun!  https://www.wildlouisianatours.com/