There is no way to currently do this with Smart Editor, and I can't think of any way to do this right now without changing the domain... hopefully someone else has ideas!
After some more thought around this I just realized you can set this up by managing the edit templates directly from the web map.
1. For example, I have a layer with edit templates set against a field with a domain. My domain has 5 values, and these are used as my edit templates for creating new features.
In the web map, click Edit and then click Manage to manage the edit templates.
Here you can select which templates to keep for editing, so for example I will only keep 1 and 5 and then save the changes.
Now when I go to edit features in the web map, I only have 2 options. Save the web map.
And now these 2 options should also be shown in Smart Editor!
Note: the value will still be available in the dropdown, but the defaults will be set to value1 or value5 depending on the templates I selected to create the feature.
Apologies I did not think of this earlier.