All you'll need is notepad, the copy function, and a steady hand.

Disclaimer- I haven't tested this at all. It might backfire horrendously, but it shouldn't. You may wish to use a more advanced editor than notepad (e.g. notepad++ or textpad) to make the edits but it shouldn't matter.

STEP 1
Open up the following file;
../Steam/steamapps/workshop/content/286500/1134969630/Config/XComContent.ini

Now add the following lines to the end of the file;

+BodyPartTemplateConfig=(PartType="Voice", Language="english", Gender=eGender_Male, TemplateName="BOIIIReaper_GethPrime", ArchetypeName="SPARK_GethPrimeVoicePackage.GethPrimeSPARKVoice", CharacterTemplate="BOIIIReaperSoldier", SpecializedType=true)
+BodyPartTemplateConfig=(PartType="Voice", Language="geth", Gender=eGender_Male, TemplateName="BOIIIReaper_GethTrooper", ArchetypeName="SPARK_GethTrooperVoicePackage.GethTrooperVoice", CharacterTemplate="BOIIIReaperSoldier", SpecializedType=true)

Save!

STEP 2
Next, open up;
../Steam/steamapps/workshop/content/286500/1134969630/Localization/XComGame.int
(don't worry about the extension, you can edit it in notepad too)

Now add the following lines to the end of the file;

[BOIIIReaper_GethPrime X2BodyPartTemplate]
DisplayName="Geth Prime"

[BOIIIReaper_GethTrooper X2BodyPartTemplate]
DisplayName="Geth Trooper"

Save!

All done. Relaunch XCOM2 and you should be able to use Trooper/Prime voices with the EWR.