Can I just have the big dents fixed?
No, If you have a loan or lien on your vehicle, your vehicle must be repair as per the insurance paperwork because your vehicle is what is securing the loan and the only security to the bank, and the bank wants to make sure their investment maintains it’s value.
Yes you can if you own your vehicle and have no loan/lien on it, however the small ones will look like the big ones when the “big” dents are only removed. Most dent technicians do not want anything to do with this type of repair because the customer maybe happy for a little while, but will eventually return. Most experienced technicians would prefer to fix it right and fix it properly.