X-rays/ultrasounds are noninvasive and are done without general anesthesia.
A biopsy just takes a second and is done with a very thin needle, the site is treated with a local anesthetic.
At the most, a pill or shot, as per the vet can be given beforehand for anxiety and to produce mild sedation, so the dog will stay still for a minute.
Panting for dogs is often indicative of pain.
I would give your vet the green light to do the tests needed to accurately diagnose the dog.
Just as with humans feeling sick and being in pain results in poor appetite.
