I often sneeze when doing the washing-up, Fairy liquid being the worse offender. It also makes my hands dry and chapped, so I did use Cussons Morning Fresh: better on the skin, but still made me sneeze, but I found W5 concentrated washing up liquid in Lidl. It's cheap and you don't need to use a lot, but still sneeze, but not so much...I might still have some coconut traces somewhere, perhaps there's some in Lidl's Formil fabric detergent that I also use. I haven't checked it fully, but the perfume is a lot less pronounced than other products that sell for a lot more money. At least there is no SLS (sodium laurel sulphate) on the list on the bottle.
This site has some info on washing-up liquids (known as dish soap in the US):
What Allergy is a British website http://whatallergy.com/