Keeping water and a rag handy is probably the simplest way to clean up and avoid using chemicals. You can keep some pieces of paper towel or a rag in a bag with a water bottle if you need to bring something with you on the go.
You can also brush and trim out dried poop clumps at home. Try putting a little powder on clumps if need be to dry them out before brushing or trimming.
You can dilute some cat shampoo with water and use that to wipe off your cat, or try a rinse-less spray shampoo like Biogroom.
You can also always give them a bath if needed. If you have a calm kitty, you can give them a “butt bath” – just dipping their backside in the sink and wiping away the poop clumps.
Some pet owners recommend wipes that are made to be more pet-friendly: – GNC hypoallergenic wipes – Burt’s Bees Cat Wipes – Earthbath All Natural Cat Wipes
Changing food. The poop in fur issue could be a result of your cat passing loose waste, which could be solved by reevaluating their diet (maybe switching to preservative and additive free), or just mixing some canned pumpkin into wet food if it is a short-term cat health issue.