I smashed my screen and need a swap out. I signed the authorisation form and they're ordering a new phone, but I don't want to swap?

A week ago I dropped my iPhone 5 and the screen shattered. I went to the apple store twice and was screwed around with wrong information about prices and the extent of the damage, eventually I was told that they can't replace the display and I will need a replacement/swap. My phone is out of warranty and I only have three months left on my contract plan. They have to order in the part and I did sign the authorisation form for store work, and in a week I have to go back so they can do the work. In short, I am wondering if I am able to back out of the replacement, or if signing that form (without any work actually being done) means I'll have to pay the $330.

Is there anything in the repair terms and conditions that says because they've ordered the part in I have to pay for it? (from what I understand they ordered a standard iPhone 5 because there were no more in stock).

I really don't want to pay $330 for something that I can live with for three months.