Welcome to the Guild, JBoucher!
It really depends on what a given mapper is looking for in a final result. Some of us hand-draw with pen or pencil, some of us draw with a drawing tablet, while some of us couldn't draw themselves out of a wet paper bag, so many depend on the capabilities of software for doing the work. There is no right or wrong method - its all good.
I like to create my coastline, mountains, rivers and other major land forms by hand (sometimes), then I scan it, color it and finish it on a PC. I have maps, though that are completely generated using software, that is drawing with a mouse, then using texture fills or even photo images to complete. The first type is usually more artistically satisfying, while the latter only takes me an hour or two to complete. It all depends on how much time I have to dedicate to a given project and how many projects I have to do.
For me, I like to hand-draw, but I hate to paint and I'm not into lineart only maps, so I need color/textures and I do that on computer.
In your case, you're making your world map for you group, and you're away, and have plenty of time to do the work. If you want to do it all by hand, great and your gaming group should appreciate it.
Truth is we love maps and mapping here, but not everyone is an artist. With the right tools and techniques cool, realistic maps can be created even by non-artists, which probably describes the bulk of members here. So we do what we can.
Post up some of your current world map so we can take a gander. Perhaps the more artistic of us can give you some direction. We all have something to offer.