How do I change the default topography of my theme without editing the CSS which I do not want to do for fear of wrecking it?
Great question, Audrey.
The correct way to change or replace the fonts used throughout your website is to edit your site's CSS, preferably via the use of a child theme. But that can be a tall order, especially if you're not comfortable editing code. You're not alone.
The next best thing would be to hire a coder to create a child theme and customize the fonts — plus anything else you may want to tweak. You can get a fast quote estimate on this page.
But, if you don't want to go that route, you can also install a plugin like Easy Google Fonts, which enables you to override the fonts used throughout your site with any font from the massive Google Font Library.
This is less than ideal, because it can negatively impact page load times. Fonts are among some of the largest files that are loaded when someone visits your site. When you use a plugin like Easy Google Fonts, your site will still load the original font with every page load, and then also load the second font, in order to override the original font used.
This can result in not only longer page load times (which negatively affects both your visitor's experience, but also your site's ranking in search engines like Google), but also a ‘flicker’ — where the text is first rendered using the original font, then re-rendered with the overriding font.
Still, it's worth a shot if you want to avoid touching the CSS in your site's theme or hiring a coder to do it for you.
Hope this helps!