Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is not permissible for a Muslim to deal with forbidden transactions in banks that deal with usury and interest, claiming that Islamic banks are not satisfactory in dealings.
Allah, The Most High, did not permit Haram (forbidden) things except in case of necessity. As Allah says: "He has explained to you in detail what is forbidden to you, except under compulsion of necessity? And surely many do lead (mankind) astray by their own desires through lack of knowledge. Certainly your Lord knows best the transgressors.” (Al-An'am 6:119)
The necessity is a condition that the pubescent person reaches and as a result consumes Haram or accepts it because if he does not do so, he will die or be closer to death. There is no such necessity in your claim.
As regards the financing that the bank dealing with interest and usury is providing, its ruling differs, according to the reality of the situation. Indeed it is the content that defines the situation not the names or titles.
If the bank takes real profit, by buying goods that its customer wants to buy, and when the goods get in its possession, it sells them again to its customer by installments even with a greater price, and then this is permissible.
But if this transaction is not real; i.e. the bank does not buy the goods and the goods are not in its guarantee, and what takes place is just lending money with interest and usury to its customer, then this is a loan with Riba and it is Haram even though it could becalled otherwise.
Allah knows best.