I have no experience with tumors, but I do have experience with lots of surgery. It's more or less like fini says. If you take only the minimum dosage for pain only, not a higher dosage to get a good buzz, just until you heal, you should be okay. That's not to say that your body won't become accustomed to it over time, and using opioids for three months will probably cause dependence.
If that happens, and you can't taper off, there is always the option for a medical detox, which is rather brief in the case of opiates. I knew one person who had to do this, but he was taking very strong stuff (fentanyl) for cancer.
People confuse addiction and dependence, however. People are usually dependent on SSRI antidepressants, for example, because they will cause withdrawal symptoms if stopped abruptly, but that does not mean that they are addicted to SSRI's.
I probably should be taking pain meds, but I am not, because the opioid epidemic scare stories make everyone paranoid, including my family, and I don't want them to worry. I stopped taking the painkillers a couple weeks post hospital discharge. I did notice a familiar small buzz as a side effect while I took them.
Talk to the doctor about your concerns, and tell him to keep an eye on the length of your usage. A couple of weeks post surgical use probably won't cause you to become dependent, but a few months certainly might.