I don't have any no-forest maps ready to use, so I haven't done any testing, but it seems to me if you just deleted/commented out the two highlighted lines (manually or via a mod), the quest would work for a trader in any biome. In fact, you can see that apparently this was set to "exclude Wasteland", but they changed it to "only Forest".
This is in quests.xml.
<!-- White River Citizen 1 - Journey to Settlement -->
<quest id="quest_whiteRiverCitizen1">
...some other stuff...
<objective type="Goto" id="trader" value="5" phase="1">
<property name="biome_filter_type" value="OnlyBiome" />
<property name="biome_filter" value="pine_forest" />
<!-- <property name="biome_filter_type" value="ExcludeBiome" /> -->
<!-- <property name="biome_filter" value="wasteland" /> -->
<property name="nav_object" value="go_to_trader" />
</objective>