Not a good idea at all.
The reason it is supposed to be unique is so that it should absolutely identify a record, not "temporarily identify a record".
Think about it: What if there are other tables which refer to this record? Unless you also update all of those, they will refer to the wrong record.
What if there are other users also accessing the database? What number are they supposed to use? The number they have loaded into memory and are about to update, or the number you just changed it to? How do they tell?
If you want a sequential number of records that changes as the records change, then add it as a different field, or use the ordinal number of the row in the table instead. Do not mess with Primary Keys - it only leads to trouble!
For example:
SELECT ROW_NUMBER() OVER (Order by InsertDate DESC) as RowNo, * FROM Tracks