First let me say that I don't use ASB and what I post below has been as a result of a few searches:
*** Check out this link -
https://support.avast.com/en-gb/article/17#idt_006In that there are a couple of things that might help.
1. Importing your default browser settings - See the Set your default browser section.
Then see - Set your default browser - This mentions.
Avast Secure Browser allows you to
import bookmarks, browsing history, search engines, saved passwords, and auto-fill form data from several popular web browsers, or from an HTML file. The highlighting BOLD is mine
For more information about importing browser data to Avast Secure Browser, refer to the following article:
https://support.avast.com/en-gb/article/83/#pcSo it would appear by importing your previous browser data if DudkDuckGo was one of the search engines in the imported data that search engine would be in the dropdown list.
This link may be useful to save:
Check out this general ASB FAQ Pages -
https://support.avast.com/en-ww/article/Secure-Browser-FAQ#pc