Birds : Hi there, vet Andrew here. I see you're offline so I'll leave this as a message for you.
Birds : There isn't much research on tumours in budgies, so that may be why your vet can't tell you for sure how this is going to pan out, and also tumours in general are often unpredictable so we find it hard to predict exactly what's going to happen.
Birds : Budgies are also poor subjects for anaesthesia, so again I can see why your vet is being cautious.
Birds : The way I see your case, you have two options, as you're clearly uneasy about the situation:
Birds : 1 - call up your vet and discuss referral to an avian specialist. These vets deal with small birds such as Charlie every day, and will have the miniaturised anaesthetic equipment and diagnostic tools needed. They may cost a little more and you may need to travel, but at the very least your vet could have a chat with them about the case and get some specialist advice. The specialist may be able to sedate her and examine the lump fully with a tiny endoscope, and from there you could be looking at surgery.
Birds : 2 - if you feel you can't afford this, then there are still options. The lump is clearly irritating Charlie, and her scratching may have set up a skin infection at the site. There are creams which can address both of these problems which your vet can prescribe. Keep an eye on the lump yourself, and report it's progress to your vet. If it's a benign tumour, it will just grow in it's place and will not cause further problems until it's big enough to block her vent, and she'll be unable to pass droppings. If it's malignant, then it may spread to her organs. In either case, monitor her appetite and general behaviour - if she stops eating and/or becomes listless and fluffs her feathers up, not wanting to do anything, then it may be the lump has got the better of her. I'm afraid it will then be time to have her humanely put to sleep.
Birds : I hope this advice has been useful; it's really the best I can do from a distance, but hopefully now you can see your options. Keep in touch, vet Andrew.