Hi again, and thank you for the additional information! : )
Each cat has a different personality and yours may just be very sensitive to any noise/motion and be more of a scaredy cat. Most cats do jump when there's a slight movement near them if they're sleeping, or dozing and not fully alert; it's the startle reflex. How old was he when he was neutered and declawed? The declawing may have something to do with it, but if you feel he's had a personality change to being afraid of everything, when he wasn't before, it would bear checking him out medically, at the vet.
The product I suggested--Feliway--should help under the circumstances you mentioned, and if need be, the vet may feel an anti-anxiety medication could help, if all else fails. I'd try all other alternatives before considering an anti-anxiety drug.
At this other website with information re: Feliway, they also discuss and sell 'flower essences'. "Rescue Remedy" is used to calm stressed cats (and people). Bach's Flower Essence Remedies (and other brands) can be found in natural food stores and places like Whole Foods Markets. Check it out, and follow the dosing information regarding pets:
If your cat is acting normally in all other ways (eating, drinking, sleeping, playing, etc.), this just may be his personality and try to do your best to make him feel safe and secure at all times. If he's not a cuddle-bug and doesn't like being petted or held, just love him on his own terms. He might outgrow this as he gets older, or this just might be who he is. Are you sure the other animals are not threatening to him when you're not around? That's a possibility to consider, also. Could a frog, lizard or insect have come into the house and frightened him? I don't know where you live, but I'm in South Florida, and my sister's cat is also skittish. She would slink into the bathroom or refuse to go in at all, to use the litterbox. We think a 'creature' may have gotten into the house and hid near her litterbox, next to the toilet and scared her a lot. Sometimes she's fine, and then she goes through periods where she acts like I described....at the times she does this, we find nothing 'scary' in the bathroom! So, you can never tell what your cat may have seen or experienced that may have caused this recent skittish behavior.
I do hope my suggestions prove helpful and he begins to relax a little more!
Keep me posted on how he's doing? Thanks!