My son did this often - the warm water relaxes the muscles around the sphincter I think. You could try a large ladle or sand shovel, I think. I know it's hard, but try not to panic or over-react, less she think poop is horrendously vile rather than a natural function. I think a really good soapy washing will take care of the spoon or other implement you use - after all, after you wipe her bum (or even your own!), you don't throw out your hands, do you??? LOL - it's more important that she see you wash properly - soap and 30 seconds of lathering is important. Turn off the water - don't let it run - a lot of kids learn to just put soap on their hands and then stick them under the water right away, which does nothing! The experts say to rub and create a lather - and kids love bubbles! - while singing the ABC song or even "Happy Birthday" twice thru to measure the right amount of time. Anti-bacterial soaps aren't necessary and actually are considered much more harmful - it's the lathering and amount of time that are really key.
You could use the plastic bag trick too - or go for doggie poop bags - put your hand inside it, grab the poop, and invert the bag, trying the top part of it in a knot. The only problem with that is, she doesn't see the poop go in the toilet where it belongs.
Just try to be matter of fact about it so she doesn't make a game out of it or completely recoil from it -- either of which will cause problems for you later on.
Hang in there - it's no fun but it will not go on forever!