Zadhan narrates from Sayyiduna Salman (may Allah be pleased with him) that it was in the Torah that there is blessing in performing wudu before eating. I mentioned this before the Prophet (peace and blessings be upon him), and he (peace and blessings be upon him) said: "Performing wudu before and after eating is a blessing."
Qays bin al-Rabi' is not a strong narrator, so washing the hands before eating is not established by any hadith.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصداق / 14604
It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "Whoever spends the night with grease on his hand and something bites him, let him blame no one but himself."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصداق / 14605
Sayyiduna Abu Hurayrah (may Allah be pleased with him) said that the Messenger of Allah (peace and blessings be upon him) said: "Whoever sleeps with grease on his hand and does not wash it, and then something bites him, let him blame no one but himself."
(b) In the hadith of Suwayd bin al-Nu'man, the Prophet (peace and blessings be upon him) and the Companions (may Allah be pleased with them) rinsed their mouths after eating sawiq; and (as in) Kitab al-Taharah, the hadith about washing the hands after eating is hasan, while washing the hands before eating is (from) a da'if (weak) hadith.
(c) Sayyiduna Abdullah bin Abbas (may Allah be pleased with him) narrates from the Prophet (peace and blessings be upon him) that he (peace and blessings be upon him) went to the toilet, and when he came back, food was brought. It was said: "O Messenger of Allah, will you not perform wudu?" He (peace and blessings be upon him) said: "Why? When I pray, I will perform wudu."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصداق / 14606