I found that if you put the reference to your JavaScript or CSS file in a Snippet instead of directly into the theme.liquid file, then it doesn't get cached in the CDN.
theme.liquid
Contains reference to the snippet between the <head> tag. For example, using a snippet named 'head':
<head>
{% include 'head' %}
</head>
head.liquid
{% capture theme_styles %}
{{ 'custom.css' | asset_url | stylesheet_tag }}
{% endcapture %}
{% capture theme_scripts %}
{{ 'custom.js' | asset_url | script_tag }}
{% endcapture %}
