Is there a way to change the default text paragraph style in WP without changing CSS by hand?
I.e. I need GUI for that.
In particular, I want to configure padding height between paragraphs.
It depends on your theme. With most themes you'll have to manually edit the CSS to do this.
But some themes have control panels that allow you to make changes to the design without editing the code. If you'd rather not write code but would like to make changes to your site, I'd suggest using a theme with design options.
Some are very simple, just a few color choices or layouts to choose from, but others have hundreds of options. There are some free ones in the theme directory like Constructor and Platform, check out the theme-options tag to see all the themes which should have control panels.
Probably I get your question wrong, but CSS is used to set values of padding. Even if you don't have any CSS with your site, what you see in the browser is the CSS the browser has built-in.
So if you want to do styling, you need to use CSS for it. There is no alternative to CSS so far, at least as long you display your site in HTML. If you instead might want to build your site in SVG, you would have other options as to use HTML+CSS. But I assume that is not an option for you.