This seems like a strange question, not sure I’m understanding. Usually people hesitate to open extra credit lines before getting a mortgage, but if you already have that then what is the concern? Do you not already have any credit cards?
You probably did not need to cancel those cards, and I’m surprised to hear you worry about dishonesty. What would be dishonest? You are allowed to have debt or credit with more than one company.
As long as you are honest on your income and debt declarations, go ahead and apply for the credit. If they don’t feel you could repay it, they won’t extend the credit. Those companies know everything :p
You don't have to close it but when then calculate what you can repay, they assume you may max out all other lines of credit as well and have to repay that too, so closing a credit card (especially a large one) can add 10's of thousands of dollars to your borrow limit.