That’s a difficult contention, since clearly Jesus relied on that oral tradition contending with Sadducees over life after death. Ref. Luke 20:27-38.
Paul who is an apostle also numbered himself among pharasees phil 3, acts 22:2-5.
I would think rather that Jesus had his own interpretation of scripture which tended to coincide and agree with the prophets and their tradition. But which included critiques of their misapprehensions of God’s will.
Perhaps your claim about oral tradition entails something else apart from the prophetic books and the position the pharisees took.
are you sure that Jesus' response in Luke 20:35-38 is from the Pharisee's Oral Torah or indeed from any Oral Torah? -- I have not read any of that in the Talmud, but that doesn't mean it isn't there.
Paul points out that he WAS a Pharisee - not that he was still. It was a sect within 2nd temple Judaism -- and the Jesus-movement was another sect until at least 132 AD
"I would rather think that Jesus had his on interpretation of scripture" -- that is what Luke 20 seems to show, not the Pharisee's point of view
To the point The ORAL Torah was later codified and expounded upon in the Talmud. - this is not my claim, but is in the Talmud itself. Rabbinical Judaism or as we call it today, simply 'Judaism' holds to the Oral Torah that was separate from the written and allowed for how to interpret the Mosaic Laws.
note though that the Apostles and Jesus rejected the ORAL Torah - this was the extrapolation of the Mosaic laws and were what the Pharisees preached. - this yes, is a claim, not specifically my own, but not Rabbinical Judaic. This claim was held by Sadducees and by Jesus movement Jews and the Essenes. It is held today by Christians and by Samaritans