Every municipality has their own building codes, but I'd be surprised if you couldn't use the setback for a walkway, even a concrete one. It generally means you can't put a structure within the setback (building, shed, pool, etc), not something just on the ground. And you're leaving out something regarding the math. If you have 20', with a 5' setback, that's usually 5' on each side, which would leave you 10', not 15'. So obviously you can't have a pool and walkways within 10'! What am I missing?
You should be able to have a 10' wide pool with 5' walkways on each side. Also, some municipalities allow variances, where you can ask them to "fudge the rules" for a good enough reason, though variances can be an uphill battle, and/or expensive.
Have a chat with your local building/planning department and ask about the possibilities. I would recommend you go down there, not try to do it over the phone. Bring a little sketch with you. Doesn't have to be fancy, just something they can look at: the shape of your property, where the house is, where the proposed pool would go. Maybe throw in some dimensions. Of course, if you come up with the previous owner's plans, that would be the place to start.
Alternately... I've seen ads for small hybrid pool/spas. Bigger than a spa, smaller than a pool, with some of the functionality of both. Some of them have jets in them that get the water moving for exercise. And they're small enough to fit in a structure that can be heated, along with the water, so it's 365-day-a-year dealio.
