... without messing up the thread?

Re-Thread it after you cut it.

If you need to just cut the threaded part shorter, the easy way is to thread a nut (preferably not the nut you'll use with it on the bike, but it'll work if it's all you can get), hacksaw the threads, file them down so there aren't any sharp edges, then take the nut off. The nut will straighten out the last little bit of the thread so that your regular nut will go right on. A slightly more elegant method is to cut and file the threaded part, then file a 45 degree chamfer on to slightly below the deepest part of the threads - if you're decent with a file, you can get the nut on easily without leaving a possible sharp burr.

If you need the threads longer, it's another matter entirely. You could get a die (which is likely to be expensive - you'll need one that's adjustable, not one of the hexagonal dies that you'll find in most hardware stores that are designed only for cleaning up threads), you'll need a die handle, you'll need threading oil (preferably sulfurized, but anything with plenty of EP additives should be fine) and you'll need tools to hold the skewer still while you cut the threads. The threads you cut will weaken the skewer, possibly putting it at risk for future breakage. You also might have to contend with hardened steel, possibly only on the outer surfaces or possibly through the thickness of the skewer. In short, I wouldn't suggest cutting the threads longer, if that's what you have in mind.

Note that you probably do not want to cut it off flush with the surface of the security nut. It is much easier to use the security "key" to tighten or loosen the security nut if there is at least 1/8" to 1/4" protruding because the security key then stays centered on the protruding bolt. This makes it easier to keep the key engaged on the indentations in the nut. Just cover the exposed end of the bolt with the rubber tips they include or, if you lost them, any good hardware store should stock these low-cost end caps.

Thanks for the clear suggestions, aley! I may not have the tools to do it myself (hacksaw and vise).
I hope to find someone this week who can do this for me.

I hear ya, Giro. I intend to have that 1/8 to 1/4" protruding beyond the nut. It's just that there is still 1" that extends beyond that point.

No vise or hacksaw are really required. I'd invest in a hacksaw blade (you can probably skip getting a whole hacksaw unless you need one anyway) and a small file. Wrap half the blade with tape (duct tape, electrical tape, Scotch tape, masking tape - whatever) and use that to cut the bolt - it'll take a little longer than using a hacksaw, but the blades are much cheaper than the whole saw and can be discarded after use if you like so you're not cluttering up your house. Put the skewer on the bike with the nut, and cut it to 1/4" or so longer than the nut. Use the file to round off the remaining end, paying particular attention to getting a nice smooth edge around the threads. Several layers of tape on the nut will keep you from scratching it up with the file if you slip. Once you're done filing, take the nut off, which will clean up any residual burrs. Double check that everything is smooth, reassemble with the rubber end caps, and go out for a ride to celebrate your successful machining job.

A hacksaw blade and a small file should be available for under $10 total for both. In a pinch, you might be able to make do with just the hacksaw blade (about a dollar) and some emery boards like what are used to smooth fingernails - I've never tried them for metal finishing, but they'd probably do just fine (and likely cost just a couple of dollars for a package).

You might want to make sure it doesn't have rolled threads on it.You may cut it off and find the proper die is too big.

I would be suprised to see cut threads on it.

Which is why proper dies are adjustable. Nonadjustable hex dies are for chasing threads, not cutting them.

Rolled threads are stronger and typically lack sharp points in the bottoms of the threads, so they're not as much of a stress riser as cut threads, generally leading to better fatigue performance. You're quite right, cut threads are unlikely on a skewer.

No die should be required for shortening threads, though.

Done! And a success! Took it to a guy at work. We put it in a vise and tried a hacksaw. (He put a nut on it first.) The blade was too dull, so he dremeled it. And I filed down any sharp points. Got it on the bike. Should be good.
Thank you all for your support.

Glad it worked! Nothing like a Dremel to knock off threads.