I would like to write: "Will you get my CV or should I send it to Ms Smith?"
In German :
Ich soll CV Frau Smith schicken
Ich soll CV zu Frau Smith schicken
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… oder soll ich Frau Smith mein CV schicken?
… oder soll ich mein CV an Frau Smith schicken?
In questions without question words, the conjugated verb is in first position in German.
It's mein CV, because the curriculum vitae is neutral in German. You can replace it with es of course. Or you use meinen Lebenslauf and replace it with ihn.
And you may use either a dative object Frau Smith or a prepositional object an Frau Smith but you have to take care about the order of objects.