It would help to know more about who you are planning to ask
Could I possibly let you have my paper at a later date /after the official deadline
Would it be possible at all to hand in my paper...
Would you mind if I handed in/sent on..
Would you not mind my sending the paper later?
will probably earn you a "Well, dear,as a matter of fact,I would."
Would you mind my [sending the paper] handing in my paper later?
is definitely much better.
Let me know if you need help with this.