In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Answering your question, Dar Al-Ifta Al-Misriyyah, states:
It is permissible to offer the istikharah before or after the witr prayer as it is permissible at any time provided it is not a time when prayer is disliked.
Almighty Allah knows best.