Want to change course chosen, how can I minimise risks?

I have applied Government and History(LV21) in LSE 2012 entry, received no offer or rejection yet. After reading more related books, I found myself love International relations more and the program is more flexible(IR students can take some government modules but not the reverse).
I was told that I can still change course choice before they have given any decision.
But I am worried that this way might lead to a straight rejection since my PS is about History and Politics(Tailor made for Oxford's His and Pol course ).

And I would like to change to the international relations and history(VL12)
Are there any feasible way for me to amend the course choice with minimal risk?
Let say transfer on Sep 2012?

There isn't really anything you can do - as you said, your PS is tailored for the current course, so it wouldn't work (especially for LSE which puts lots of emphasis on PS) even if you could. However, since it's after 7 days, you can't change your choices anyway.

Unis, and top ones even more so, would also be very reluctant for you to change your course when you enrol (assuming you get and meet your offer) - they offered you a place in the course you chose for a reason. The only thing you could do is withdraw completely this year and re-apply next year when you've figured out what exactly you want to study

Agree with the rest of it, but the bit in bold isn't necessarily true - within the same university, you can ask them to consider you for a different course at any time.