I doubt that the ‘Arabs’ were responsible for the limitations considering that many Palestinians were willing to accept about 350,000 Jewish refugees in 1946. The ‘Arabs’ did not need to exert pressure on anybody anyway considering that the Zionists did not want to receive a mass of ordinary Jews:

In the Zionist Congress which took place in London in 1937, Dr. Weizmann established the line of policy with his words:

“The hopes of Europe’s six million Jews are centered on emigration. I was asked, ‘Can you bring six million Jews to Palestine?’ I replied, ‘No’…From the depths of the tragedy I want to save two million young people…The old ones will pass. They will bear their fate or they will not. They were dust, economic and moral dust in a cruel world…Only the branch of the young shall survive…They have to accept it.”
(Holocaust Victims Accuse, p. 25)

“Palestine cannot absorb the Jews of Europe. We want only the best of Jewish youth to come to us. We want only the educated to enter Palestine for the purpose of increasing its culture. The other Jews will have to stay where they are and face whatever fait awaits them. These millions of Jews are dust on the wheels of history and may have to be blown away. We don’t want them pouring into Palestine. We don’t want Tel Aviv to become another low‐grade ghetto.” (Quoted in The Jewish Press, October 18, 2002)

Yitzhak Gruenbaum was chairperson of the Jewish Agency's Rescue Committee.

“When they asked me, couldn’t you give money out of the United Jewish Appeal funds for the rescue of Jews in Europe, I said, ‘NO!’ and I say again, ‘NO!’…one should resist this wave which pushes the Zionist activities to secondary importance.”
(In Days of Holocaust and Destruction, by Yitzchak Greenbaum)

(Emphasis added. Source and more here.)

Not only did the Zionists play down the Shoah as it was happening, but they had no respect for the survivors either. For the Zionists, the Shoah was a confirmation of their philosophy at best, and a distraction at worst.

If indeed Palestine was partially responsible for the Shoah by refusing immigrants, then logically many other nation‐states would also become Shoah perpetrators, such as Switzerland and Imperial America. Although somehow I doubt that Herzlians would welcome such a consensus.