I used a Shuttle GP2 for 2 years, and I always used Valvoline can remember exact number but it was a valvoline mineral oil.
Whilst i was using it I got a transmission oil light, even that I put valvoline. People warn to use HMMF but even after putting valvoline i did 50,000KM no problems.
Anyway answering the question, I have also once put Toyota hybrid oil when in a service at Automiraj. But a specialized oil by a company that has been manufacturing engine oil for a long time cant let you down.