Need to check this closely. I had to research this in detail before I flatbedded my 2003 dually.
Dually chassis cabs have 2 different dually axle widths - a 66.8" track standard or a 74.7" track width with the GTY RPO option. The 74.7" track width is the same as what the dually pickups get. Track width is from center line between left duals to centerline between right duals. If the axle you're looking at is the narrow version, I don't think you'll be able to relocate the spring pads wide enough to fit your 2002 dually pickup.
The 3500 chassis cab rear frame width is 8" narrower from outside of the left rear leaf spring to outside of the right rear leaf spring vs. the 3500 pickup frame and accommodates the narrower rear axle.
If you want to verify all this yourself, check out the GM upfitter guides - it's all laid out in great detail with dimensioned drawings. Here's the book for the 2009 trucks, see pages 67-70 for the numbers I've listed above (Upfitter guide numbers are in mm)
https://www.gmupfitter.com/files/media/photo/417/2009_HD_CK_FS_CC_071713.pdf
The upfitter book for your 2002 and all other years is here as well.
https://www.gmupfitter.com/pages/body-builder-manuals
Bottom line, if the 2009 donor chassis cab vehicle has the GTY RPO option, I think it will work under your 2002 if the spring perches are moved. If it's the narrow axle, no dice.