All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If you are asking about what is obligatory as in the question, then it is not obligatory to raise your hands in any part of the prayers, not in the Witr prayer, or in any other prayer. Even in the obligatory prayer, it is not obligatory to raise the hands when saying the Takbeeratul Ihraam (the initiating Allah Akbar). What is obligatory is to say the Takbeeratul Ihraam.
Ibn Qudaamah said: “We do not know any difference of opinion that it is (only) recommended (desirable) to raise the hands at the beginning of the prayer...” [End of quote]
An-Nawawi said: “The (Muslim) nation has unanimously agreed that is recommended to raise the hands in the Takbeeratul Ihraam and Ibn Al-Munthir, and other scholars, reported the consensus (of the scholars) on this issue...” [End of quote]
Therefore, if you are asking about the desirability of raising the hands at that position (Witr), then if you pray the Witr prayer three rak'ahs with one Tasleem (saying Salaam to conclude the prayer), then in this case you also pray with one Tashahhud and not with two Tashahhuds, so that it does not resemble the Maghrib prayer because it is mentioned in the Hadeeth: “Do not pray the Witr three Rak’ahs and make it resemble the Maghrib prayer.” [Al-Haakim]
The scholars mentioned that if one prays the Witr three Rak’ahs with one Tashahhud only, then the prohibition mentioned in the Hadeeth (resembling the Maghrib prayer) is not applicable.
Hence, if you pray with one Tashahhud, then it is not legislated to raise your hands when standing up for the third Rak’ah because the Hadeeth of 'Abdullaah ibn ‘Umar to which you referred to that includes raising of the hands when standing up after having prayed two Rak’ahs, then this is in regard to standing up from the first Tashahhud, whether it is a four-Rak’ah prayer, or a three-Rak’ah prayer –which is the Maghrib prayer.
Al-Bukhaari entitled a chapter in his book: "Chapter of raising the hands when one stands up after the second Rak'ah"; Ibn Hajar said commenting on this Chapter: "This refers to rising after the Tashahhud. This does not included the case when one does not sit for Tashahhud and stands up from the Sujood (prostration) to another Rak’ah, because of the general meaning of the narration before this one (which states), 'and he does not raise the hands when he raises his head from the Sujood (prostration)'.” [End of quote]
Allah knows best.