How to combine custom-select styling with chained select

[chechu]

1) Script Title: chained selects

2) Script URL (on DD): http://www.dynamicdrive.com/dynamici...menu/index.htm

3) Describe problem:
On this page I used this custom-select styling: https://www.w3schools.com/howto/howto_custom_select.asp
On the same page there is a contact form on which the custom-select works fine. But how to make the same visual adjustments on the chained select that is in the sidebar?
Adding class="custom-select" does not do the trick.

[chechu]

Anyone, please?