In your situation, I would start with a hand saw to remove the bulk of the material, then use a jack plane to finish it. That's what I did on my first paddle and I think it took me 30 minutes or so for each of the tapers. The results were excellent, it just takes more time and perspiration than using power tools.

Kudzu is absolutely correct about needing SHARP tools and frankly, most people new to using hand tools have no concept of what a truly sharp tool is. He wasn't exaggerating about the plane needing to be "shaving sharp". If you don't have good sharpening equipment already, you'll need to invest in it. Trust me, once you try a really sharp tool and experience what a joy it is to use. you'll fall in love with hand tools. I've found that most people who have become frustrated with hand tools simply have never used one that's truly sharp.

Over the past few years, I've accumulated a lot of sharpening gear, from grinders, to power sharpeners (Makita and Work Sharp), waterstones (Japanese and Norton), sandpaper on glass, a granite surface plate (surprisingly inexpensive), jigs from multiple manufacturers (Veritas jigs are great!) and so on. I've also reconditioned and sharpened quite a few old tools (which is why I have so much sharpening gear, or at least that's what I tell myself) and tuned/sharpened a bunch of new, low-end block planes and spokeshaves for classes. One of these days, I'm going to write reviews of them and post them on my book's website, but that's another subject.

Of the sharpening systems out there, I think the Lie-Nielsen method is the simplest and most effective one, provided that you're starting with a blade that's in reasonable shape (doesn't require grinding). It was developed for woodworkers who are more interested in using their tools than sharpening them (there are a lot of "sharpening geeks" out there) and it produces a mirror-polished, shaving-sharp edge in a few minutes with a minimum of equipment (a flat surface, one grade of sandpaper, a dual-grit water stone, a simple honing guide and a small steel rule). Once sharpened, re-honing a dulled blade can accomplished in a minute or so. Here are links to their instructions for sharpening and for making their angle setting jig/stone holder:

http://www.lie-nielsen.com/pdf/Sharpening.pdf
http://www.lie-nielsen.com/pdf/AngleSettingJig.pdf

If you can't afford their "Basic Sharpening Set" (it's an investment you won't regret), you can substitute less expensive sharpening media for the waterstone, such as sandpaper on a glass plate or granite slab. The results won't be quite as good, but they will certainly be good enough to produce a very usable edge.

Here's a link to the set: http://www.lie-nielsen.com/catalog.php?sku=1-SK

Whatever method you end up using, being able to sharpen your tools is an invaluable skill.