There should not be much risk of using a cleaner wax by hand other than maybe some sore muscles. There is not to much risk using a DA either, just a little. I would think you should see some improvement, but don't expect mind blowing results if you are doing it by hand of course. The water spots might prove to be a bit more difficult, depending on what type they are.
You could divide the car up in to sections and work one per day if trying to complete the whole car in one day is too much. It will make it a little less stressful for you knowing you are just trying to complete one section, like the front end, instead trying to finish the whole car in one go, then realizing half way though the day that you are not going to be able complete it. That way you can relax and take your time and enjoy the process and results.
The amount of time it is going to take you depends on how long you decide to work a section. And how long you work a section will affect your results. If you do a simple wipe on/wipe off, it won't take long but your results won't be that noticeable.
No need to be to afraid of a DA. After you try this by hand you will realize how much you will want one to help you out. Just keep reading around here and you will have the info you need to ease those fears.
Oh, and try your cleaner wax out on a test spot as many on here recommend. Tape off a two foot square, or smaller, or just one simple line of tape. This will give you an idea of the results you will get for the amount of time you have worked the product and allow to compare it directly to an unworked area. With out the tape your test spot will blend into the uncorrected area and not show the true contrast of worked vs. unworked. It will also give you an idea of how hard it is to buff out the wax residue. Some products are meant to be wiped off fairly soon after working and can be really hard to remove if you leave it on there until you finish the whole car. Temperature and humidity can affect products too.
I have not used Meguiars Cleaner wax, but I would assume it is no too temperamental.