neither the carpet or the cotton upholstery is dirty, She says she gets it cleaned every year because of the dander from (you guessed it) her white cat
Are there any feathers inside the couch???
Have you tried to see what is inside the piping??? ( I asked this becasue my overconfidence made me not inspect properly last year and i ended up recovering some cushions for a client of mine.
Is there any cat smell on the couch??
any how, any shampoo that is been made for Tahitian cotton would be appropriate to clean it safely. An all fiber rinse or 24oz of white vinegar in you 5 gallon jug will do the rinsing just fine.
I must warn you and go to the job prepared. Do not over wet cotton It will take a long time to dry and you will have great chances to get browning on it. Bring some air movers and speed dry it. Pay special attention to the piping and if you can don't get it wet clean it a t the end with a damped terry towel. I know the super experienced and know it all will tell you it is very easy and it is (in a way ) but it is easier to damage it if not guided with the proper precautions.
If there is cat ( not urine) smell in the couch boost your shampoo with sodium percarbonate ( hydrogen peroxide) and that will help you rid the smell easier without the use of other expensive products.