Settling 2nd mortgage
No, you should not get delinquent on both the mortgages. Have you explained your current situation to your lender? I think you should try mortgage modification or refinancing first. In case you're not able to refinance or modify your mortgage, then you can think about settling the second mortgage. Yes, usually lenders don't agree to settle debt unless you're delinquent. It will be difficult to settle the second mortgage. However, you should not lose hope.
I assume that you don't have any home equity. Even in such a situation, you will be liable for paying off the second mortgage in full. If you wish, you can request for a loan modification with your lender to get an affordable repayment plan to pay off the debts. You won't be able to refinance the mortgage in any way as there's no equity in the property.