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.
Thank you for your question.
As you said in your question, there are slight differences regarding prayer times between schools of jurisprudence, i.e., between the Hanafi and Shafi`i, Maliki and Hanbali schools. All of them are correct.
As for the time of `Asr, according to the Hanafi school, the time for `Asr enters at two shadow lengths. The other three schools of thought state that it enters at one shadow length. As such, the Hanafi `Asr time enters a bit later than the Shafi`i one. Both positions are sound and have their proofs in the primary texts. You can follow any of these opinions; they both are correct.
May Allah accept your and our good deeds!
Allah Almighty knows best.