Fully booked train

We have just arrived in Tokyo with our JR Pass and had some problems in booking the seats on the chosen trains for our itinerary.

In particular, the Shinkansens from Hakodate to Tokyo on the 15th seem fully booked on all times. Since this is the last day of our 7 days pass, we need to travel on that day and won't mind to stand if necessary.

Our question is therefore the following: do you think we could plan to take the planned Shinkansen anyway, expecting to stand, or is there a risk that we could not get on the train at all?

Thank you
Luisa