There is really no need to feed into a seperate container. The risks really outweigh the benefits.
I hope you don't leave the rat unattended! There is nothing wrong with feeding live, I have done it before, but prefer F/T because it is more convenient (ex: I don't have to go out and get live feeders, I just freeze a bunch). Just make sure you keep an eye on that rat while it is with your BP, don't want any nasty bites.