Yeah, you can alter the whole theme without using the Theme Editor. Or any of the WP files. Here's a piece of advice: Even if you used the one-click install to install WP (or any program), download the install file and extract it, so you have a copy on your hard drive to work from. You should edit files on your hard drive to match any changes you make on the site (or change them on your hard drive, then upload to your site via FTP; that way, you always have a copy of what's on your site).
Anyway, go into the wp-content folder, then click on the themes folder, and choose the theme you're using. You can also put new themes in that folder, if you don't want to alter the default, classic and any other themes in there. But if you do want to alter them, you just go into the folder of the theme you want to change (i.e., default). You can change the style.css file in it on your hard drive and upload it to your site in the same folder, letting it overwrite the old file. However, if you want to make changes not set by the style sheet, you'll want to learn more about designing themes, which is also available on the WP codex.