Hacking the core is never recommended, since you’ll have to reapply your hack every time you update (and for a number of other reasons).
The first thing I would normally do is to check if there is a hook or filter to allow you to modify the date. It doesn’t appear there is one.
The next thing you might check is whether the function you’d like to change is in the list of Pluggable Functions (functions that WordPress lets you override) – http://codex.wordpress.org/Pluggable_Functions – and that function doesn’t appear to be.
So, my suggestion would be to create a custom date field (the Advanced Custom Fields plugin works great for that). Then if you need to sort by date, you’d just have to set your query to sort by that custom meta field rather than the standard post date field.