Hi Mani,
If you want to choose and pay off open items without due date you can run your F110 in the same way your are doing now. But in next payment date put in 12/31/9999 (mm/dd/yyyy) format.
Then all items which are due as well as not due will be selected for payment.
In additional criteria you can use, document type, partner bank details, etc. to limit your search and include documents in payment run.
Let us know if it suits your need.
Thanks,
Subhrajit