Hi.. Is there a way to change the style of Related Action buttons in Records?

Are you talking about the Shortcuts (which launches a related action) available on the Record Views? If so, afaik they can't be customized.

If you have upgraded to 7.10 then you have the option of applying the theme which will help you. Refer to link forum.appian.com/.../Themes_for_Embedded_Interfaces.html

I wonder if it's possible - though the 'Shortcut' on the Record View resembles a button, it isn't a standard button component exposed to us for usage by any means.