I haven't come across a case such as yours where the funds available only narrowly meet the requirement. But I have followed the rejections thread very closely, and as far as I know nobody was rejected for a case such as yours. That doesn't mean it can't happen, but I think it's rather unlikely.
It all depends on what you are most comfortable with. I probably wouldn't draw unnecessary attention to whoever is paying the fee by mentioning it in the LoE, but maybe you could get your dad to pay the fee anyways so that your funds will remain untouched? If CIC then have any questions while processing your application, you can show them you still have the same amount of money as before.
Lastly, you probably know this already, but you only need to pay the processing fee. The "right of permanent residence fee" can be paid once your application is approved.