TL;DR My cat panics when I try to put him in a harness and I'm not sure if he's just afraid of his harness or if I'm doing something wrong. Are there any tips on buying cat harnesses? Is there something I can do to make him more comfortable with the harness?
Some background:
My aunt has a dog and a cat and, when she leaves on business trips, she brings them to my place and I look after them. I have a hedgehog and the dog is (rightfully) skeptical about bugging her after he got too close to her. The cat is curious, but knows not to bug her. So I'd say they all get along, essentially. I have to walk the dog every day, and the cat always tries to get out around the time that I go to take the dog out.
I can get the cat to come back (he's pretty obedient, despite being a troublemaker), but he seems to get lonely if the dog isn't around with him. He tends to misbehave when I leave to take the dog on walks (scratches furniture, meows a lot so the neighbors complain, disturbs my hedgehog to the n-th degree) whereas if I go to work and come back, he's usually pretty good (plays with toys, sleeps, leaves my hedgehog alone). My aunt is going away for a little longer than usual, and my apartment neighbors are normally lenient about the cat when my aunt leaves for a week or so, but I can't subject them to constant meowing for a month.
Furthermore, my hedgehog is used to quiet and dislikes when a shadow lurks overhead, like most hedgehogs do. The cat makes a lot of noise and jumps on her enclosure very often when left alone. If this were to happen continuously for a month, I think my hedgehog would get sick from stress. I do usually move her out of the living room and into the bedroom when the cat is around, but she still gets pretty stressed from the cat meowing more (and louder) than usual. Also the door doesn't lock, so the cat can still get into the bedroom. In my eyes, leaving the cat at home is not an option.
This summer, my aunt is leaving her cat and dog with me for a few months (she says it could extend into next year) and is going to be living out of the country, although not permanently. I'm pretty sure I should be dealing with this problem now, so I figured the best thing to do is learn to walk the cat. I'm looking after them now while my aunt is out of the state, and I've bought everything I need to start walking the cat.
I'm having difficulty, though, since I can't get him on a leash/harness. He does want to go outside, and if we're just in my yard he's pretty much safe, but he tends to get fussy when I use a leash/harness. Usually I can get him to do pretty much anything, but he hates this for some reason. He only put it on once without complaining and since then he's been a nightmare. I thought it might be too tight and brought him to the pet store to have them check, but they determined it was a good size and let me swap out for a set made of a different material after the ordeal we went through trying to get the harness on him. (They thought the material was itching him.) It isn't working. Surprisingly, he doesn't seem to be too upset with me even though I'm usually the one subjecting him to this.
Right now, I take the cat in a cat carrier while I walk the dog and I've been going to a park with fewer dogs in preparation for when the cat is ready to walk on a leash. I could probably keep that up, but he's miserable whenever he's in the cat carrier. How can I make him less frightened of his harness? Is there something I should be considering when looking for one outside of just the size and material?