No you wouldn't pay the equivalent of 20 yrs interest, you only pay interest for the time you have the loan, it's calculated daily on the outstanding balance so if you accelerate the payments on a 20yr loan by paying the relevant payments for a 10yr one then it will finish in 10yrs as though it was that term day one.
The only difference is you will need to take out a 20yr mortgage protection policy initially anyway, you may be able to cancel it and swap for a 10yr one afterwards but bank will have to have one in place for the term applied for unless you are in the exempted categories.