Even considering the nature of the cat, many cat owners are happily walking their very happy cats on a harness, walking jacket or leash. It may sound impossible, but it can be done with some patience, (OK, maybe a LOT of patience) and your cat can get a whole new life, safely enjoying the outdoors and getting much needed exercise at the same time.
Training your cat to the leash is best done in small steps. First, allow the cat to get familiar with the leash by placing somewhere it can be sniffed and evaluated. Then, in baby steps, put the leash or walking jacket on your cat.
Your cat may get scared the first few times venturing outside. This does not mean that your cat can not learn to walk on a harness. Be patient, and make the outside encounters as quiet and interesting as you can. Keep them short as well. A short fun time outside will make a good impression on your cat.
Remember, this is all new to your cat and can be quite frightening. Taking it slow will pay off.
Don't buy a leash that is designed for a small dog, but instead look into purchasing a leash or lead that is specifically designed with a cat in mind. These leads wrap around your cat, giving you control of the cat and keeping the cat from choking itself in a frantic attempt to get away.
You might want to practice on the lead at home a few times, although most cats will not like this at all. Don't let this deter you from trying it outside, because for some cats the fact that they are outside is enough to make them tolerate the leash or lead. The cat might get so wrapped up in exploring the great outdoors that it doesn't really notice the lead very much anymore, and this is the ideal situation.
While persistence and patience pays off in making your cat get used to not only a leash and harness, but also going outside, if it is obvious that your cat is not getting less stressed and is indeed suffering, then maybe you are better off finding some other way for your cat to enjoy the outdoors.
Trying for some time in baby steps is the way to be successful, but there are cats who just won't have any part of this. Be observant. If your cat gets a little more comfortable each and every time, then continue taking her out. Short trips with lots of praise and treats.
However, before long you may be surprised at your cat. She may begin to see her safe outside excursions as a highlight of her day. Something fun, interesting and stimulating to break up the monotony of being inside.