Hydrocodone is an opiate, in the same class as morphine. However, it is a relatively weak medication. It could, technically, be addictive if taken for long periods of time or if not taken as prescribed. However, I wouldn't worry
about this in your case! It is likely that your dentist
will just give you 2 or 3 days worth of the hydrocodone. It would be impossible to become addicted to such a small amount of the medication. They idea that your dentist has is just to give you enough strong pain medicine so that you are comfortable for the first few days after the procedure when the pain and swelling are at their worst.
However, if this idea makes you uncomfortable, then go ahead and talk about it with your dentist again. Many people can get by after a wisdom tooth procedure with just standard anti inflammatory medications like ibuprofen or naprosyn. These medications do slightly raise the risk of bleeding
a bit from the surgery site, however. So you would have to talk to your dentist to make sure that they are ok with taking these medications.
Good luck with the procedure, and please ask all of your questions of your dentist!