[cypher]

It is always hard to see hams age & Buzz really is quite an old man now so some problems like weight loss & drying of the skin with possibly some fur loss are to be expected.
You can try things like flax seed & evening primrose oil to help with his skin & fur, add in extra high fat foods like seeds & nuts more frequently can help maintain weight, a little baby food, porridge or mashed veg is often appreciated by elderly hams too.
I do think the lump is your biggest concern & I agree that it would be best to take him to the vet, anything growing that fast does need attention & as velma said could quickly begin to cause him discomfort or pain.
Discuss your concerns with the vet, most good vets will only see having any animal PTS as something to be done only when there are no other options & quality of life is too poor , they won't normally suggest that just because Buzz is old without good reason.