If you prefer not to use the appletloader, or if you have other dlls you want to distribute besides the lwjgl natives, it is possible to do it yourself.
I have not done this before, but I believe the basic idea is to pack your DLL's into the JAR, then programatically copy them onto the user's computer. To gain access for copying the files, your JAR must be signed. This lets the user chose whether or not to give your applet access to his computer. There are a lot of guides online for how to sign a JAR, but I have not found an easy one to follow. The process seems to be extremely complicated and counter-intuitive, so unfortunately I can't help you out much with that part.
The other thing you would need to do, is to have your applet determine if the user's computer is running Windows, Mac, or Linux. The dynamic libraries for each OS are different. For example, in the lwjgl library, the natives consist of DLL's for Windows, SO's for Mac, and JNLIB's and DYLIB's for Linux.
I was thinking since the developers of lwjgl have done it when they created the appletloader, you might be able to get some help on the lwjgl forums,
http://www.lwjgl.org (although I have not found them to be very useful in my opinion). Might be worth a shot.
Oh, BTW, if you prefer to just use the appletloader, I can help you out with that, since I have had experience using it, and I know what kind of problems you might run into.